United States
Environmental Protection
Agency
Environmental
Research Laboratory
Athens GA 30601
EPA-600/3-78-029
March 1978
Research and Development
Simulation of
Nitrogen Movement,
Transformation, and Uptake
in Plant Root Zone
Ecological Research Series
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the ECOLOGICAL RESEARCH series. This series
describes research on the effects of pollution on humans, plant and animal spe-
cies, and materials. Problems are assessed for their long- and short-term influ-
ences. Investigations include formation, transport, and pathway studies to deter-
mine the fate of pollutants and their effects. This work provides the technical basis
for setting standards to minimize undesirable changes in living organisms in the
aquatic, terrestrial, and atmospheric environments.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/3-78-029
March 1978
SIMULATION OF NITROGEN MOVEMENT,
TRANSFORMATION, AND UPTAKE
IN PLANT ROOT ZONE
by
James M. Davidson
Donald A. Graetz
P. Suresh C. Rao
H. Magdi Selim
University of Florida
Gainesville, Florida 32611
Grant No. R-803607
Project Officer
Charles N. Smith
Technology Development and Applications Branch
Environmental Research Laboratory
Athens, Georgia 30605
Technical Advisor
Arthur G. Hornsby
Source Management Branch
Robert S. Kerr Environmental Research Laboratory
Ada, Oklahoma 74820
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GEORGIA 30605
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DISCLAIMER
This report has been reviewed by the Environmental Research
Laboratory, U. S. Environmental Protection Agency, Athens, GA,
and approved for publication. Approval does not signify that
the contents necessarily reflect the views and policies of the
U. S. Environmental Protection Agency, nor does mention of trade
names or commercial products constitute endorsement or recom-
mendation for use.
11
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FOREWORD
Environmental protection efforts are increasingly directed
towards preventing adverse health and ecological effects associ-
ated with specific compounds of natural or human origin. As part
of the Athens Environmental Research Laboratory's research on the
occurrence, movement, transformation, impact, and control of en-
vironmental contaminants, the Technology Development and Applica-
tions Branch develops management and engineering tools for asses-
sing and controlling adverse environmental effects of nonirriga-
ted agriculture and of silviculture.
Surface and ground waters may, under certain conditions, be
adversely affected by the accumulation of nitrate resulting from
the application of nitrogen fertilizer to agricultural lands to
increase crop production. Because of its water pollution poten-
tial, it is important to understand the fate of nitrogen in the
plant root zone. This report presents a detailed research model
that describes the movement, transformation, and plant uptake of
nitrogen in soils. Because of the complexity of the research
model, a simpler, user-oriented management model that requires
minimal input data was also developed. Both simulation models
are useful management tools for predicting the behavior of nitro-
gen and for assessing nonpoint sources of pollution.
David W. Duttweiler
Director
Environmental Research Laboratory
Athens, Georgia
111
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ABSTRACT
Two simulation models, a detailed research-type and a con-
ceptual management-type, for describing the fate of nitrogen
in the plant root zone are discussed. Processes considered in
both models were: one-dimensional transport of water and water-
soluble N-species as a result of irrigation/rainfall events,
equilibrium adsorption-desorption of NHi*, microbiological N-
transformations, and uptake of water and nitrogen species by a
growing crop.
The research-type model was based on finite-difference
approximations (explicit-implicit) of the partial differential
equations describing one-dimensiona], transient water flow and
convective-dispersive NHi, and N03 transport along with simul-
taneous plant uptake and microbiological N-transformations.
Ion-exchange (adsorption-desorption) of NIU was also considered.
The microbiological transformations incorporated into the model
describe nitrification, denitrification, mineralization and
immobilization. All transformations were assumed to follow
first-order kinetics. The numerical solution was flexible in
its soil surface boundary conditions as well as initial con-
ditions for soil-water content and nitrogen concentration dis-
tributions in the soil profile. The numerical solution can be
used for non-homogeneous or multilayered soil systems.
The research-type model contains a detailed description of
the individual processes and requires a large number of input
parameters, most of which are frequently unavailable. Because
of this, a less detailed management-type model employing several
simplifying assumptions was developed. The management-type
model requires a minimal number of input parameters, and pro-
vides an integrated description of the behavior' of various
nitrogen species in the plant root zone.
This report was submitted in fulfillment of Grant No.
R-803607 by J. M. Davidson, D. A. Graetz, P. S. C. Rao, and
H. M. Selim, University of Florida, Gainesville under the partial
sponsorship of the U. S. Environmental Protection Agency. This
report covers the period March 10, 1975 to March 9, 1977, and
work was completed as of March 9, 1977.
IV
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CONTENTS
Foreword iii
Abstract iv
Figures vi
Tables. , . . ix
Acknowledgments ..... x
1. Introduction 1
2. Conclusions 5
3. Recommendations 7
4. Research Model 9
Equations for Water Flow 9
Nitrogen Transformations 11
Nitrogen Transport and Transformations. .... 14
Solute Transport in Multi-Layered Soils .... 18
5. Models for Plant Uptake 21
Plant Uptake of Water . . . 21
Plant Uptake of Nitrogen 25
Root Growth Models 30
6. Management Model 34
Transport of Water and Nitrogen 34
Nitrogen Transformations 40
Nitrogen Uptake 44
7. Research Model Simulations .... 46
Transport and Transformations . 46
Transport, Transformations, and Uptake 52
Summary 60
8. Management Model Simulations 61
Model Verification 61
^Model Simulations 63
References 67
Appendices
A. Description of the Computer Program for the
Research Model 77
B. Flow Chart of the Computer Program 82.
C. FORTRAN IV Program Listing 83
D. Kinetic Rate Coefficients for Nitrogen
Transformations 99
E. List of Publications Resulting from this
Project 104
v
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FIGURES
Number
1 Soil nitrogen transformations considered in the
research model. The subscripted symbol k is
a first order rate coefficient, while the sub-
scripts e, s, i, and g refer to exchangeable,
solution, immobilized, and gaseous phases,
respectively. KD is the Freundlich distribu-
tion coefficient
Soil-water content (6) and soil-water suction (h)
versus depth in a clay-sand soil profile. For
A the water table is at x = 100 cm, and for B
it is at a great depth (x-*00) ............ 18
Adsorbed and nonadsorbed solute relative effluent
solute concentration (C/Co) distributions from
unsaturated clay-sand soil profiles. Open
circles were calculated based on average soil-
water content within each soil layer, while
the solid and dashed lines were calculated
using the soil-water content shown in Figure
2A and 2B ..................... 19
Evapotranspiration (ET) as a fraction of potential
evapotranspiration (PET) with time as simulated
by the Molz-Remson (M-R) and the Nimah-Hanks
(N-H) models .................... 27
Root length density distributions for corn (£ea
mays L.) at selected times during the growth
season as calculated by the empirical model .... 33
Distribution of soil-water (solid line) and
nonadsorbed solute (dashed line) after 5 and
10 cm of water had infiltrated into an
initially dry (6.^=0) soil profile ......... 35
Distribution of soil-water (solid line) and
nonadsorbed solute (dashed line) after 5 and
10 cm of water had infiltrated into a soil
profile at a uniform initial water content
(0i, shown as vertical dashed line) of 0.1
cnr/cm3 ...................... 36
vi
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Number Page
8 Agreement between dsf/dwf and 8j_/6f as cal-
culated by Equation (50) and experimental
data from various sources 37
9 Comparison between measured (solid circles) and
predicted (solid lines) position of a nonad-
sorbed solute front in a sandy soil at various
times. The soil was planted to millet
[Pennisetum americanum (L.) K. Schum] 41
10 Simulated soil-water content distributions in a
deep uniform loam soil profile during infil-
tration and redistribution of soil-water 47
11 Simulated solution-phase concentration distri-
butions of NOs-N and NHi+-N in a deep uniform
loam soil profile during infiltration and re-
distribution of soil-water. The rate co-
efficient for nitrification (ki) was 0.01
hr.-1 48
12 Simulated solution-phase concentration dis-
tributions of NOs-N and NHit-N in a deep
uniform loam soil profile during infiltra-
tion and redistribution of soil-water.
The rate coefficient for nitrification (ki)
was 0.1 hr."1 * 49
13 Total amounts of NEU-N and NOs-N in a deep uni-
form loam soil profile during infiltration
and redistribution of soil-water. The nitri-
fication rate (ki) was 0.01 or 0.1 hr"1. These
plots were derived from the simulated data
presented in Figures 11 and 12 50
14 Simulated soil-water content distributions during
infiltration and redistribution of soil-water
in a loam soil profile with an impermeable
barrier at a depth of 40 cm 51
15 Simulated solution-phase concentration distribu-
tions of NHi,-lSF and NOa-N during infiltration
and redistribution of soil-water in a loam soil
profile with an impermeable barrier at 40 cm
depth. The kinetic rate coefficient for deni-
trification (ki) was 0.01 hr"1 52
Vii
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Number
16 Total amounts of NO3-N remaining and total amount
of N released by denitrification during infil-
tration and redistribution of soil-water in a
loam soil profile with an impermeable barrier
at a depth of 40 cm. The denitrification rate
coefficient (kO was 0.001 or 0.01 hr"1
17 Simulated soil-water content distribution in a deep
uniform loam soil profile during infiltration
and redistribution following three irrigation
events "
18 Simulated NO3-N solution concentrations in the soil
profile at selected times following three
irrigation events (Figure 17) 55
19 Simulated NIK-N solution concentrations in the soil
profile at selected times following three
irrigation events (Figure 17) 56
20 Soil-water content (6) distributions with time
during plant-water uptake and evaporation in
a uniform soil profilq of Lakeland soil (from
Selim et al.89) 57
21 Percent of applied nitrogen remaining within the
plant root zone during the simulated growth
season. The curves were based on data presented
in Figures 18 and 19 58
22 Comparison between simulated cumulative nitrogen
uptake and that when maximum uptake demand is
satisfied at all times during the growth season . . 59
23 Fraction of applied nitrogen remaining in the plant
root zone of Maury soil, simulated by the manage-
ment model, during the corn growing season 62
24 The predicted depth of nitrate front under three
water application schemes during the growing
season in a sandy soil profile. Increase in
the maximum root zone depth (L) with time is
also shown 54
25 Cumulative nitrogen uptake by corn grown in a
sandy soil under three water application
schemes, as simulated by the management model ... 55
Vlll
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TABLES
Number Page
1 Comparison between soil-water content (G)
profiles during an 8-day period in a sandy
soil as simulated using the Molz-Remson
(M-R) and the Nimah-Hanks (N-H) models for
plant uptake of soil water 26
2 Comparison between measured nitrogen uptake
by corn (Zea mays L.) grown under field con-
ditions and that predicted by three simula-
tion models 63
3 Kinetic transformation rate coefficients for
various nitrogen species in selected soils 1Q1
IX
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ACKNOWLEDGMENTS
The assistance' of Dr. Luther C. Hammond (University of
Florida), Dr. Ron E. Phillips (University of Kentucky), and
Mr. Ron E. Jessup, and Mr. William G. Volk (all of University
of Florida) is gratefully acknowledged. Also, the cooperation
and overall project coordination by Mr. Charles N. Smith (EPA
Environmental Research Lab., Athens, GA) as the Project Officer
and by Dr. Arthur G. Hornsby (Robert S. Kerr Environmental
Research Lab., Ada, OK) as Technical Advisor is appreciated.
The project investigators wish to express their apprecia-
tion to the Center for Environmental Programs in the Institute
of Food and Agricultural Sciences at the University of Florida
for financial support during the project period. The project
investigators are also indebted to their colleagues in the
Department of Soil Science at the University of Florida for
their assistance and suggestions during the development of the
simulation models presented in this report.
x
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SECTION 1
INTRODUCTION
Nitrogen is an essential element for all biological pro-
cesses. In an undisturbed environment the cycle of synthesis,
consumption, and decay of nitrogenous compounds takes place
without increasing or decreasing the total nitrogen content in
the system. This delicate balance is disturbed when man
separates the areas of nitrogen assimilation (plant and animal
growth and development) from areas of consumption and waste
accumulation (large metropolitan areas). Because of this
separation, most agricultural soils now require supplementary
applications of nitrogen fertilizer to maintain high yields
and profits. These commercial nitrogen applications may, under
certain conditions, adversely affect water quality through
significant accumulations of nitrate in surface and ground water,
Therefore, the fate of nitrogen in the plant root zone is of
interest not only because of its use in biological systems, but
also because of its water contamination potential and quantity
and petroleum energy required for its commercial production.
The fate of nitrogen at and below the soil surface is
governed by a variety of interrelated and complex processes.
Various inorganic (NH^ , NOs, NOa, NjO and N2) and organic
nitrogen forms exist simultaneously in the soil. These and
other nitrogen substrates undergo reversible and/or irreversible
transformations owing to chemical and microbiological processes.
The water-soluble nitrogen species (NtU, NOs, and NOa) may also
be transported through the soil in response to soil-water move-
ment. The NHi» and NOs distribution is complexed further by
absorption by plant roots. The extent of water and nitrogen
uptake by plants is determined, in part, by the transpiration
demand, which in turn is dependent upon plant species, growth
stage, and meteorological conditions. Soil microhydrologic
properties also influence the rate at which water and nutrients
are transported through the soil to the root surfaces.
The complexity of the soil-water-plant system is further
enhanced by the fact that all of the above processes are tran-
sient in nature and occur simultaneously. The relative impor-
tance of these processes in determining nitrogen behavior is
dependent not only on several physical, chemical and biological
soil properties, but also on the plant species and the growth
stage of the crop. Therefore, a prerequisite to modeling the
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fate of nitrogen in soil-water-plant systems is a complete under
standing of the nitrogen transformation processes. A consider-
able amount of qualitative information is available regarding
nitrogen and its agronomic aspects and individual processes in
soils.1 However, due to the nature and conditions under whicn
much of this research was conducted, it is difficult to i
this information into a form that can be used to develop
relationships which are required for simulation and/or prediction
purposes.
The degree of sophistication and detail in any simulation
model is determined by (i) the understanding of the system to
modeled, (ii) the modeler's conceptualization of system processes,
(iii) the modeling approach and error bounds in the approxima-
tions required to solve the problem, (iv) the data base avail-
able for input into the model and verification of the model, and
(v) the intended application of the model. When the system
processes are initially unknown and the model is designed on the
basis of inductive reasoning, the approach is referred to as
"black box" modeling. On the other hand, when a complete
quantitative description of the system to be modeled is avail-
able and the model is deduced from established laws, a "white
box" approach is said to be utilized. Thus, depending on the
completeness of the knowledge of the system, mathematical models
may be considered as having various "shades of gray"—the darker
the shade of gray, the less is known about the system.
Mathematical models to describe physical, chemical, and
biological processes are generally of three distinct types. A
stochastic model assumes the processes to be modeled obey the
laws of probability. Empirical models are designed on the basis
of experience and observation and the use of regression equations
which correlate input with output parameters. Mechanistic models
are based on well established physical, chemical and biological
laws that describe individual processes. Mechanistic models are
versatile in that extensive historical records are not required
for their development. However, these models require a complete
understanding of the process or system being described. A fre-
quent limitation of mechanistic models, therefore, is an inade-
quate understanding of the system. Empirical models are of
assistance in such situations since they identify parameters
which influence the system being described.
OBJECTIVES AND SCOPE OF THIS STUDY
Intensive research efforts by several researchers during
the past decade have yielded a multitude of models for simula-
tion of nitrogen behavior in soil-water-plant systems. However,
due to the limited understanding of major processes and the
interrelationships among them, considerable divergence exists
among the modeling approaches undertaken. A state-of-the-art
review3 of nitrogen simulation models indicated that these models
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range from totally empirical to those that are mechanistic in
nature. The major objective of the work presented in this
report was to evaluate and design comprehensive models for
describing the behavior of nitrogen in the plant root zone.
A systems analysis concept, i.e., an examination and
mathematical description of important processes that function in
the system, was employed in developing a mechanistic model de-
scribing the fate of nitrogen in the plant root zone. Empirical
models were also used when necessary because of the vast com-
plexity of the problem and the lack of a thorough understanding
of the system.
The modeling efforts in this study were conducted on the
basis that two distinct groups of individuals are interested in
predicting the behavior of nitrogen in the plant root zone. The
research model is mechanistic and requires a detailed description
of the individual processes and a precise knowledge of the input
parameters. The research model was useful in understanding the
complex interactions among various processes and in identifying
major contributing parameters. The research model described in
this report is flexible and can incorporate other transformation
and transport processes in addition to those presented. The
computer time required to simulate an entire crop growing sea-
son is quite large for the research model (see Appendix A for
details). Furthermore, the values of several parameters and
coefficients required in the research model are generally un-
available for most sites. For this reason, an alternate model
for management purposes was developed from the research model.
Several simplifying assumptions were made in order to save com-
puter time. The management model was developed so that a mini-
mum amount of input information was necessary to provide an
integrated description of nitrogen behavior in the plant root
zone during a growing season. The loss of accuracy resulting
from the simplification and assumptions made in developing the
management model was estimated with the research model. Both
models are modular in nature and allow changes to be made in
individual process descriptions without altering the basic
structure of the total model.
REPORT FORMAT
A mechanistic research model is presented in Section 4 for
simulating nitrogen transport and transformation during tran-
sient unsaturated water flow in soils. Mathematical relation-
ships used tp describe water and nitrogen uptake by plants are
described in Section 5. The management model and its assump-
tions are discussed in Section 6. Simulations obtained from the
research model are presented in Section 7. Simulations obtained
from the management model are discussed in Section 8. A de-
scription and FORTRAN IV computer program listing for the re-
search model and a list of publications resulting from this
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project are given in the appendices. A table of transformation
rate coefficients for various nitrogen species in selected soi /
compiled from a literature search, is also included in the
appendices.
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SECTION 2
CONCLUSIONS
A thorough literature search was conducted to identify the
mathematical relationships being used to describe the fate of
nitrogen species in the plant root zone. The results of this
initial effort provided the direction and emphasis for the proj-
ect. In so far as possible, mathematical relationships that had
been verified and used with some degree of success were incor-
porated into our modeling effort. Several conclusions can be
made based upon this study.
(1) Current experimental data base is inadequate to ver-
ify mathematical models for describing the behavior of nitrogen
species in the plant root zone with time. Soil fertility experi-
ments to establish optimum yields generally include very few, if
any, soil-water and nitrogen content distributions and plant-
nitrogen uptake measurements with time. Also absent in these
studies are soil-water characteristic measurements for the soils
on which the experiments were conducted. Cooperative experiments
involving various disciplines need to be initiated and measure-
ments must be made during the crop growing season.
(2) Soil-water plant root uptake models of Nimah and Hanks
and Molz and Remson were evaluated and shown to predict similar
soil-water content distributions with time in the absence of
plant-water stress. Due to differences in conceptualization of
plant response to water stress in these two models, predicted
soil-water content distributions differed in the presence of
water stress. The two models could be made to predict identical
soil water uptake patterns if plant water stress was defined
similarly in both models.
(3) The management model was in general agreement with the
research model when simulating the total quantity of a given
nitrogen species in the plant-root zone. Because of the number
of coefficients and computer time required to simulate a growing
season, the management model has considerable appeal. Also,
because of soil spatial variability it is difficult to obtain
coefficients which represent the soil profile.
(4) Increasing the first-order transformation rate co-
efficients by 100% increased the amount of nitrate produced in
a given time period by a maximum of only 17%. A similar
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Difference was observed when all rate coefficients were assumed
constant with soil depth rather than a function of organic matter
and water content with depth.
(5) The research model is a valuable tool for evaluating
conceptual nitrogen transformation processes in the soil profile.
The model is flexible and designed for maximum research use.
(6) The level of knowledge on water and nitrogen uptake
by plant roots is inadequate at the present time for modeling
these processes at the microscopic level. Root growth and
distribution characteristics are also too inadequately understood
to formulate mechanistic models at this time. Therefore, in this
study it was necessary to use a macroscopic model to describe the
uptake of water and nitrogen by a relative root distribution.
This approach agreed with experimental data.
(7) Temperature was not included in our models, not because
of a lack of understanding of how temperature influences nitrogen
transformations but because of the difficulty in modeling tem-
perature fluctuations at the soil surface during the growing
season. As the plant canopy increases, the insulation to the
soil surface changes making it difficult to model with any
degree of accuracy the temperature at the soil surface with time.
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SECTION 3
RECOMMENDATIONS
This project has identified some major difficulties in
describing the fate of selected nitrogen species in a biologi-
cally active soil. Based upon these observations, research
areas requiring immediate attention before quantitative mathe-
matical relationships can be applied with confidence are pointed
out. The following recommendations and/or suggestions were
developed by the project investigators.
(1) Careful laboratory experiments involving the uptake
of water and nitrogen by plants should be conducted with special
attention given to measurement of root growth and root distri-
bution and location of the water and nitrogen uptake by the root
during the growing season.
(2) Careful field and laboratory experiments need to be
conducted to develop a data base to provide input parameters for
mathematical models describing the fate of nitrogen in the soil
profile. Measurements should include soil-water content, nitro-
gen species, root distribution, and cumulative nitrogen uptake
with time and soil-water characteristics of the soil used in
the study. Water and nitrogen inputs as well as climatic
environmental conditions should be well-defined during the
growing season. It would be best if these studies were con-
ducted using research personnel from several disciplines.
(3) The output from various available simulation models
need to be compared. Due to significant differences in the
conceptualization of the soil-water-plant system and initial
and boundary conditions assumed in each model, it is frequently
difficult to compare the output from simulation models.
(4) The importance of spatial variability should be con-
sidered with regard to the sophistication needed in our current
mathematical modeling efforts for nitrogen. Current research
on spatial variability suggests that differences in nitrogen
distribution with depth in the field may be as great as an
order of magnitude.
(5) The models developed in this study need to be ex-
panded to include mineralization of plant residue and organic
waste. This would require a more detailed description of
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microbial populations and biomass with time. Some procedures
have been developed but none have been verified and shown to
be accurate for different environmental conditions.
(6) The management model needs to be improved in order to
consider nonhomogeneous or multilayered soil profiles as well as
to allow for prediction of concentration distributions of nitro
gen species within the root zone.
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SECTION 4
RESEARCH MODEL
In this section, a mechanistic research model is presented
for describing simultaneous transport and transformations of
nitrogen species during transient unsaturated water flow through
soils. A model for simulation of transformations during steady-
state water flow was also devised under the auspicies of this
grant; a detailed description of the latter model is available
elsewhere.1* It should be emphasized that the research model
presented in this report is flexible and can be adapted to in-
corporate other processes which influence water and nitrogen
transport and nitrogen transformations in soils. Processes such
as partial displacement of soil-water due to water channelling
(Quisenberry and Phillips5) or due to the presence of mobile and
immobile water (van Genuchten and Wierenga ) are not included in
this study.
EQUATIONS FOR WATER FLOW
The nonlinear partial differential equation governing one-
dimensional flow of water in unsaturated soils may be written as
(see Kirkham and Powers7, Selim et al.8):
narwv,\3h - 9 ir^i3h 8K(h)
CaP(h)FE ~ 9¥ K(h)3¥ "
where,
9 = soil-water content (cm3/cm3),
h = soil-water head or suction (cm),
K(h) = soil hydraulic conductivity (cm/day)
z = distance in soil, positive downward (cm),
t = time (days) /
Cap(h) = soil water capacity (cm"1).
In equation (1) the soil-water capacity, Cap(h), is a
measure of the change of soil-water content with water head
(Cap(h) = 86/3h) which is determined using soil water character
istic relationships (8 versus h).
The initial condition of nonuniform soil-water content in
a semi-infinite soil column is stated as:
-------
h = h (z,0) 0 < z < « (2)
The boundary condition at the soil surface (z=0) is a constant
(or variable) water head H:
h = H z = 0 t <_ ti (3)
which describes continuous water infiltration for a time t]..
Following the cessation of water infiltration, i.e. for times
greater than ti, the boundary condition is:
qz=0 = -K(h) || + K(h) , z=0 t>tj (4)
which describes water redistribution under a constant (or vari-
able) evaporative water flux q _n at the soil surface.
Z"~" \J
In order to obtain a numerical solution for equation (1)
subject to conditions (2) to (4) , we express these equations in
finite-difference approximation form. In this study, the
explicit-implicit finite difference scheme (Carnahan et al.9;
Salvador! and Baron10) was used. We refer to a discrete set of
points in the (z,t) plane given by a grid with spacings Az and
At, respectively. Grid or mesh points are denoted by (i,n) where:
z = i Az, i = i, 2, 3, ...
t = n At, n = 1, 2, 3, ...
The finite difference approximation for the water flow
equation (1) is:
Cap(h) [h - hn] = Y K<
K(hn+l/2) Ihn+l _ hn+l,
- hn] (5)
where y = At/2(Az)2 and g = At/Az.
Numerical solutions to the water flow equation are presented by
Davidson et al.11 and Selim et al.8 for similar finite-difference
explicit-implicit approximations.
10
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NITROGEN TRANSFORMATIONS
The microbiological nitrogen transformations considered in
this model were: (i) nitrification of NIU to N03, (ii) minerali-
zation of organic-N to NHi* , (iii) immobilization of both NHit and
NO 3 to organic-N, and (iv) denitrification of NO 3 to gaseous
forms. In addition, ion-exchange of NHi* was also considered.
These processes are summarized in Figure 1. The ion-exchange
process was considered to be instantaneous, whereas all other
processes were of first order kinetic type. The rate coef-
ficients associated with these first-order reactions were ki,
k2, k3, k.4 and k5, respectively, for NHi* nitrification, N03
immobilization, NHi» mineralization, NHif immobilization and NOs
denitrification (day"1).
Although nitrification follows the sequential oxidation
pathway of NHij-^NOa-^NOs , the NOa ions are rapidly oxidized to NOs
in most soils. Hence, nitrification may be considered as a
single-step process with the NHi^NOa step controlling the rate
of NO 3 production.
Mehran and Tanji12, Hagin and Amberger13, Beek and Fris-
sell11*, and Misra et al.15 have all used first-order rate equa-
tions to describe transformations of nitrogen. Environmental
(NHJ
K
D
(NHJ
4's
3k4
(Org-N)
k
(N
3>s
5
2
N20)g
Figure 1. Soil nitrogen transformations considered in the
research model. The subscripted symbol k is a
first-order rate coefficient, while the subscripts
e, s, i, and g refer to exchangeable, solution,
immobilized, and gaseous phases, respectively.
Kn is the Freundlich distribution coefficient.
11
-------
factors such as soil-water content, temperature, pH, and
aeration have significant effects on nitrogen transformations.
In this study optimum conditions with regard to pH and tem-
perature were assumed. However, submodels may be added as
necessary to take into account the influence of these P
on the rate coefficients. Optimum temperature for most .
formations is between 30° to 35°C. Neutral pH is optimal r°f;
a majority of the transformations. It was assumed in this stu y
that agricultural soils will have pH values between 5.5 ana /.u.
The major limitation in selection of a rate coefficient for
nitrification appears to center around the selection of a vaiue
that represents the activity of the microbial population re
sponsible for nitrification. However, because of the relative
speed of conversion of NH% to N03, it is believed that the
error introduced by not using the correct rate coefficient tor
this process may introduce only a small error when simulating
long time periods for known NHi* inputs.
Based on the nitrogen mineralization potentials of a large
number of soils, Stanford and Smith16 concluded that the
cumulative amount of nitrogen mineralized followed a first order
rate equation. Moreover, Stanford et al.1 showed that the
mineralization rate coefficient (k3) varied with temperature in
an exponential fashion. In this study, the transformation rate
coefficients were chosen to represent an average temperature
during a period of 2-3 weeks. The model can be adapted to in-
corporate changes in the rate coefficients owing to soil
temperature. However, temperature distributions in the soil pro-
file and in the crop canopy with time would be the required input
parameters.
First-order rate processes have been used by Mehran and
Tanji12 and Hagin and Amberger13 to describe denitrification in
soils. Hagin and Amberger15 included the effect of pH, tempera-
ture, oxygen and organic carbon content in their simulation of
denitrification. In this project, oxygen diffusion as a con-
trolling mechanism for denitrification was not included since it
required additional parameters describing oxygen exchange in the
root zone (respiration) as well as oxygen diffusion properties
in the unsaturated soil profile. It should be pointed out that
several investigators have reported denitrification rates which
were independent of nitrate concentration (zero order kinetic)
over a fairly wide range.18'19'20 Bowman and Focht21 have ob-
served that many of these studies, however, were conducted at
relatively high nitrate concentrations where zero-order reactions
would be expected.
The kinetic rate coefficients for nitrogen transformations
are frequently assumed to be constant12'15, although their
magnitude depends upon several soil environmental factors.
12
-------
McLaren22 suggested that these rate coefficients are dependent
upon the size of the microbial population responsible for the
transformation. The population and/or activity of any group of
microbes is determined, in part, by the energy source available
at any given depth in the soil profile. Based upon this, Rao
et al." assumed that the magnitude of k decreased exponentially
with depth in a similar fashion to the organic matter content
distribution in the soil profile.
The transformation rate coefficients are also dependent
upon the soil-water content (6) or soil-water suction (h) .
Selim et al.23 have developed the following empirical relation-
ships, similar to those used by Hagin and Amberger13, using
published data (Miller and Johnson2
and Myers26)
Stanford and Epstein
f!(h)
(6a)
where,
fi(h) =
k2 = k2
0 ;
O.OOS(-h-lO);
0.2+0.006(-h-50);
0.5+0.0015(-h-100);
1.0-0.002(-h-433);
h > -10 cm
h > -50 cm
h > -100 cm
h > -433 cm
h < -433 cm
k3 = k3 f3(h)
where,
0.25 + 0.0064(50+h) ; h > -50 cm
f3(h) =
kit =
0.25 + 0.005(-50-h) ; h < -50 cm
1.0
; h < -200 cm
and,
ks = k5 f 5 (OM,h, 9)
where ,
f5(OM,h,6) =
(6b)
(7)
(8a)
(8b)
(9)
(10a)
0
'OM ( z) ]
OM
maxj
fQ - °'8 0satl
0.1 9 .
sat
OM(z)/OMmax)
; (9/9sat)<0.8
,o.8<(e/esat)o.9
13
-------
Note that in equations (6a) through (lOb), ^ for i = 1 to 5 ar
constants, 9 is saturated water constant, and 0Mmax £•» tn®i:L
maximum sac mineralizable organic-N content in tne so
profile. The functions f. (i = 1 to 5) are empirical represeu
tations which describe xthe dependence of the transformation
processes on 9, h, and/or OM.
NITROGEN TRANSPORT AND TRANSFORMATIONS
The movement of water-soluble nitrogen species through soil
occurs as a result of molecular diffusion and mass transport
the soil-water phase. Because of the general acceptance or
chromatography theory and its applicability to soil-water sys
tern, this approach was used to describe the vertical movement
and distribution of water-soluble nitrogen species in a soil
profile. The partial differential equation for transient one-
dimensional solute transport and simultaneous transformations
is (Selim et al.23):
3(6C.) a 3C. 3(qC.) 3S.
1 0 _/~ « 1 J- - ± $. (11)
_ D
p
at
where C. is the solution concentrations of the i nitrogen
species (yg/cm3), D(6,v) is the dispersion coefficient (cm2/day) ,
q is the Darcy flux (cm/day) , v is average pore-water velocity
(cm/day) and obtained from q/9 , p is soil bulk density (g/cm3),
S. is adsorbed solute phase of the ith nitrogen species (yg/g) ,
and $ . describes the biological transformations influencing the
•h Vi ^~
i nitrogen species.
The mobility of the ammonium (NHi* ) ion in a soil-water
system is directly influenced by the adsorption-desorption of
NHit* within the soil matrix. Numerous equations have been used
to describe adsorption-desorption, but the most common are the
Freundlich, first-order kinetic, and Langmuir equations (David-
son et al.27). Other types of cation exchange equations that
could be used to describe the adsorption-desorption of NHi,"1" are
described by Dutt et al.28 Thermodynamically based adsorption-
desorption equations require more information about the com-
position of the soil solution than is generally available. It
is believed that simpler adsorption models can be used as
reasonable approximations for the adsorption-desorption of NH4
in many soil-water systems.
Assuming a linear Freundlich adsorption for NHi» + and first-
order rate processes for the nitrogen transformations shown in
Figure 1, equation (11) can be rewritten in the following form
for NHit+ and N0a~ in the soil solution (Selim et al.23):
14
-------
^ m ^\-£ TI v* ^ Tfc
oA o A V oA P
RTTT = D - 75- TV— -kiA-kitA + Trks (OM)
o t r\ 2 w d z "
•^\T3 CV^ T2 \T ^ °D
O-D __ O -D V 0 H5 111
where, A = concentration of NHlf+ in soil solution (yg/cm3),
B = concentration of N03"" in soil solution (yg/cm3),
OM = amount of mineralizable N in organic phase (yg/g),
klf k2, k3, k4, ks = kinetic rate coefficients, respective-
ly, for NHt(+ nitrification, N03~ immobilization, NHij"1"
mineralization, immobilization of organic-N, and N03~
denitrification (day~M
V = q(z) - 9-|| - D||, where q(z) is the Darcy water flux
(cm/day),
R = 1 + pK /9, retardation factor23 for NH^* exchange,
K_ = distribution coefficient for ion-exchange (cm3/g),
such that E = KQA where E is amount of NHn. in ex-
changeable phase (yg/g).
The transformation processes for organic N are described by:
= k2 8 B + k^ 6 A - k3 p(OM) (14)
u u.
and the gaseous loss of N due to denitrification is calculated
from:
plf = ks 6 B (15)
where, G is the sum total of N20, NO, and/or N2 gas (yg/g).
Finite difference approximations for the nonlinear partial
differential equation governing transport and transformations of
NO3 and NHi,, respectively, may be expressed as follows23:
B"*1 - B; = yDf1/2 [
[Bn+1 - 2Bn
,.. /n x ., ,_. _-, . , .. ,
- (V/6) $ tB ~ Bi^ + kl At A
- (k2 + ks) At
15
-------
and,
- (v/e)f 1 B
j + k4) At A^ + k3(p/0)At OM?
The initial condition of a nonuniform nitrogen concentration
distribution in a semi-infinite soil column may be stated as:
A = A (z,0) 0 < Z < ~
B = B (z,0) 0 < Z < °° (18)
OM = OM(z,0) 0 < Z < «
For nitrogen transport and transformation, equations (12) and
(13) , the boundary condition considered was that of a continuous
solute (NEU or NOa) flux where:
= q CI z = 0 t <_ t2 (19a)
qB - D- = q CII Z = 0 t < t2 (19b)
a Z —
where, CI and CII are the applied solution concentrations of
NHit and NO 3, respectively. When application of these solute
solutions is terminated (i.e. t>ta), equations (19a) and (19b)
are also used with CI and CII equal to zero (provided that t
The finite difference approximations for water, NOs , and
NH"» transport (equations (5) , (16) , and (17) , respectively) are
nonlinear since the values of Cap (hn+1//2) , K(h1?+1//2), and Dn+1/2
n+1 11 i
are dependent on h. for which solutions are being sought. The
iteration method described by Remson et al.29is frequently used
to predict hn+ ' using hn. Selim and Kirkham30 showed that the
solution of the water flow equation could be approximated satis-
factorily using h , and a smaller At than required for a stable
solution. This simplifies the computation considerably since
the system of equations becomes linear. Accordingly, the
following approximations were made:
Cap(hJ+1/2) = Cap(hJ)
16
-------
K
(hn+l/2} =
Dn+l/2 = n
i x
Incorporation of the appropriate initial and boundary
conditions in their respective finite difference forms and re-
arrangement of equations (5) , (16) , and (17) yield three linear
systems of equations. In matrix-vector form, each system of
equations yield a tridiagonal real matrix associated with a real
column vector. The absolute value of each main diagonal co-
efficient is greater than the raw -sum of the off-diagonal co-
efficients in the matrix. Hence, the matrix for each system of
equations is diagonally dominant (Varga31). Therefore, each
matrix is nonsingular and a unique solution exists.
To satisfy the convergence criteria in solving equations
(5) , (16) , and (17) , the increments Az and At were chosen such
that
Az < D /V
— max max
At 5 Az/2vmax
where Dmax' Vmax' Kmax' Capmax are the maximum values °f D< v<
K, and Cap at any time step.
Thus far we have presented numerical solutions for water
flow (equation [1] ) , and the NHit and NO 3 transport and trans-
formations (equations [12] and [13] ) . In, order to complete the
nitrogen transformation processes, it is necessary to solve for
exchangeable NH^ (E) , organic-N (OM) , and gaseous-N (G) at every
time step and incremental distance in the soil profile. This
was achieved as follows:
En+1 = KDC, (20)
OM
:n+1 = OM? + (At/p) [k2 e Bn+1 + k, e An+1
(21)
- k3 p OM?]
Gn+1 = Gj + (At/p) ks 9 Bj+1 (22)
17
-------
SOLUTE TRANSPORT IN MULTI -LAYERED SOILS
For the research model discussed thus far, represented by
equations (1), (12), and (13), the soil profile has been assumed
homogeneous with respect to soil physical properties and solute
adsorption characteristics. Most soil profiles, however, are
multi-layered or nonhomogeneous in nature. Therefore, a separate
study was initiated to develop a simulation model for describing
solute transport through a saturated and unsaturated multilayered
soil profile. The model was based on finite-difference approxi-
mations of the convective-dispersive equation for solute trans-
port (see eq. 11). Details of model development are reported by
Selim et al.32. The major features of the model and conclusions
reached are presented in the following discussion.
Figure 2 shows the soil water content (9) and soil water
suction (h) distributions in a soil profile consisting of two
distinct layers, clay and sand, each having equal lengths (Li =
L2 = 50 cm) . The case where the water table was at a finite
depth L = 100 cm is illustrated in Figure 2A. The case where
the water table was at depth x+oo, i.e. the bottom layer having
a great length, is shown in Figure 2B. The steady state soil-
water content (6) and water suction (h) distributions for the
clay-sand soil profiles shown in Figure 2 resulted from a con-
stant flux (q) of 0.072 cm/day at the soil surface. The satu-
rated water content (6 t) of the sand and the clay layer were
0.40 and 0.55 cm3/cm3, respectively.
Water Suction h, cm
Water Suction h.cm
0 20 40 60 80 100
100
0 .1 .2 .3 .4 .5
Water Content e
oc
w
£60
15 80
t/)
mo
D
20 40 6O 80 1C
B /
h/
Clay /
Sand T
I
e
X)
/
e
0 .1 .2 .3 .4 .5
Water Content e,
Figure 2. Soil-water content (6) and soil-water suction (h)
versus depth in a clay-sand soil profile. For A
the water table is at x = 100 cm, and for B it is
at a great depth (X->°°) .
18
-------
Effluent concentration distributions (relative solute con-
centration, C/Co, versus effluent pore volume, V/Vo) for a non-
,adsprbed and adsorbed solute exiting the soil profiles in Figure
2 at x = 100 cm are shown in Figure 3. For the nonadsorbed
solute, the concentration distributions were similar regardless
of the position of the water table. In contrast, concentration
distributions for the adsorbed (first order kinetic adsorption)
solute were distinctly different. A lower average regardation
factor exists for the soil profile having a water table at x =
100 cm (Figure 3). The average soil-water content in the soil
profile with a water table at x = 100 results in a lower re-
tardation factor in comparison with the case where the water
table was at x-><». Note that because of the marked differences
in soil-water content distributions, the pore volumes VQ were
significantly different among all cases considered.
1.0
0.8
J0.6
U
0.4
0.2
0
UNSATURATED FLOW
No Adsorp.
Kinetic Adsorp.
CLAY-* SAND
water table
at x =100 cm
— at x = co
01 2345
V / V0
678
Figure 3. Adsorbed and nonadsorbed solute relative effluent sol-
ute concentration (C/Co) distributions from unsatura-
ted clay-sand soil profiles. Open circles were calcu-
lated based on average soil-water content within each
soil layer, whereas the solid and dashed lines were
calculated using the soil-water content shown in
Figures 2A and 2B.
19
-------
If the water content distributions (Figure 2A and B) we£e
considered uniform, with an average water content within eac£ion
individual layer, the problem of solute transport and adsorp nt.
through unsaturated multilayered soil profiles can be signir^
ly simplified as discussed in the previous section. The °?
circles in Figure 3 are calculated concentration distr .Ij1 ater
for adsorbed and nonadsorbed solutes when an average so^_ that
content within each layer was assumed. These results sno™ so±i-
for all unsaturated profiles considered, the use of average
water contents (open circles) provided identical concen^a^°
distributions to those obtained where the actual water content
distributions were used (dashed and solid lines). Thus, wnen
a steady water flux (q) is maintained through a layered son
profile, concentration distributions of adsorbed and nonaasoroeq
solutes at a given location in the soil profile can be predicted
using average soil-water contents. Results from laboratory
experiments using adsorbed and nonadsorbed solutes and layered
soil columns (Selim et al.32) support these findings.
Based on the above results, it was concluded that average
microhydrologic characteristics for a soil layer can be used to
describe the movement of solutes leaving a multilayered soil
profile. This conclusion supports the assumption that uniform
soil-water content can be used to represent each soil layer in
order to simplify the solute transport problem. The above
findings were helpful in modifying the research model to con-
sider multilayered or nonhomogeneous soil profiles.
20
-------
SECTION 5
MODELS FOR PLANT UPTAKE
The inherent complexity of the crop root zone and the
dynamic nature of water and nutrient uptake by roots defies an
exact mathematical description at a "microscopic" level. How-
ever, there have been several attempts to accomplish this
difficult task. On a simplified scale, the root system can be
represented by a line sink of uniform strength (absorptivity).
The water transport equation for this case, written in cylindri-
cal coordinates, has been solved for a variety of initial and
boundary conditions. Depending upon the restrictiveness of the
conditions, analytical solutions3' as well as numerical solu-
tions31*'35 to the flow equations are available. However, due
to a lack of experimental data that characterize many of the
crop parameters at a microscopic level, these models generally
have not been verified.
In other modeling efforts, the microscopic flow processes
near a root are ignored and the entire root system is treated as
a distributed sink of known density or strength36 39. These
macroscopic models have been able to provide an integrated de-
scription of soil-water extraction by crops grown under field
conditions1*0 and to simulate the effects of irrigation water
and soil salinity on crop production"*l . Microscopic models, on
the other hand, have been useful in identifying soil and crop
parameters that are significant in determining water uptake by
plant roots35.
PLANT UPTAKE OF WATER
After an extensive literature search, the models proposed
by Molz and Remson37'38 and Nimah and Hanks39 for describing
soil-water uptake by plant roots were selected for further
evaluation.
The process of soil-water flow to roots is ignored in macro-
scopic modeling approaches, and water extraction by plant roots
is treated as a sink in the one-dimensional transient water
flow equation:
-W
-------
where ,
6 = volumetric soil-water content (cm3/cm3) i
D(9) = soil-water diffusivity (cm2/day) i
K(9) = soil hydraulic conductivity (cm/day) /
t = time (days) ,
z = soil depth (cm) / v Of
W(z,6,t) = a sink term (day'1) to account for uptaKe u
soil water by plants.
Several functions have been postulated for W(z,9,t).
form proposed by Molz and Remson3^ is:
D(6) R(z,t)
W(z,6,t) = (ET) fL
D(9) R(z,t) dz
where ,
ET = volumetric evapotranspiration rate per unit soil
surface area (cm3/cm2/day) ,
L = depth of bottom of root zone (cm), and
R(z,t) = "effective" plant root distribution function which
is proportional to the root density distribution.
It should be recognized that equation (24) is an empirical
model that distributes the evapotranspiration demand (ET) over
the entire root zone according to the product [D(9) R(z,t)]. The
transpiration demand (ET) could be made to vary with time.
The form of the plant water uptake sink term [W(z,t)] used
by Nimah and Hanks39 is:
[H + (RRES-z) - h(z,t) - s(z,t)] R(z)-K(9)
where, Hr is an effective root water potential; RRES is a root
resistance term and the product (RRES-z) accounts for gravity
term and friction loss in Hr; h(z,t) is soil-water pressure
head; s(z,t) is the osmotic potential; Ax is assumed to be unity
and is the distance from plant roots to where h(z,t) is measured;
Az is soil depth increment; R(z) is proportion of the total root
activity in the depth increment Az; and K(9) is the hydraulic
conductivity.
Major drawbacks of the Molz-Remson3 7 approach are that they
assume (i) all soil water to be available for plant root ex-
traction, and (ii) that the evapotranspiration demand will be
satisfied by the plant roots, regardless of the soil water
status in the soil profile. The Molz-Remson model was modified
during this project to overcome these two drawbacks. First, the
22
-------
total available water (TAW) to plant roots was defined as that
water contained in the soil profile between "field capacity"
(9pC) and 15-bar water contents (615),
TAW fL ,Q n . , ,-,.*
(8-615) dz (26)
Jo
Second, the evapotranspiration demand (ET) was set equal to
potential evapotranspiration rate (PET) calculated from a Pen-
man type model when available water (AW) in the profile was
greater than or equal to 20% TAW. The value of ET was decreased
linearly to zero when AW was less than 20% of TAW.
ET = PET AW >_ 0.2 TAW f271
ET < PET AW < 0.2 TAW
The modification used in equation (27) was based upon the experi-
mental data of Ritchie*2. The potential evapotranspiration
demand (PET) on any given day of the growing season was calcu-
lated by a Penman-type model 3 . The value of PET was further
adjusted by multiplying it by a "crop factor" to account for
changes in crop water uptake demand during the season (Blaney
and Griddle"*) .
The simple case of soil-water uptake by plant roots front a
"static" soil profile (i.e., no vertical flow of water) was
simulated using the Molz-Remson model as well as the Nimah-Hanks
model. The soil profile was assumed to be at a "field capacity"
soil-water content (0pc) of 0.08 cm3/cm3 throughout the root
zone, while 615 was set equal to 0.03 cm3/cm3. Thus, the total
plant available water, as defined in equation (26) , in the root
zone (L=100 cm) was equal to 5 cm of water. The K(6) function
used was :
K(6) = Exp[-3.3470~°'62 + 10.1753] (28)
The root length distribution in the soil profile was described
by :
R(z) = [3.384] [Exp(-0.035z)] [Sin(0.031415z)] (29)
and was assumed not to change during the 8-day simulation period.
Note that the value of R(z) is equal to zero at z=0 and 100 cm
with a maximum root density at z=23 cm. The potential evapotran-
spiration demand (PET) during the simulation period was assumed
constant at 0.6 cm/day.
For the case described above, equation (23) reduces to:
i = -W(z,0,t) (30)
23
-------
where, the changes in soil-water content (8) are only due to
plant uptake. The functional forms proposed by Molz~R^m
(equation 24) and Nimah-Hanks (equation 25) were used to
the sink term w(z,6,t). In the evaluations presented in tn
report, the D(9) function. in equation (24) was repla£ Changes in
function due to a greater sensitivity of the latter
e.
®q*
The value of effective root water potential (Hr)
(25) is an unknown. Nimah and Hanks estimated its
every time step by successive iterations to make the
uptake of water over the entire root zone equal to tne
tion demand. This process continued as long as Hr was n g
than the potential below which the plant would wilt. inu ,
the Nimah-Hanks model, 0 < Hr < Hwilt = I5 bars- Tne ? ™t^
of having to "search" for~an appropriate Hr value can be avoiae
by solving equation (25) explicitly for Hr in the following
manner and noting that :
PET (t) =
(31)
Substitution of equation (25) for W(z,6,t) in equation (31) and
assuming Ax=Az=1.0, yields:
PET(t) = r[Hr+(RRES-z)-h(z,t)-s(z,t)] R(z) K(6) dz
o
(32)
Equation (32) may be expanded to :
PET(t) = H
R(z) K(6) dz + RRES
z R(z) K(6) dz
h(z,t) R(z) K(6) dz -
s(z,t) R(z) K(6) dz
Rearranging equation (33) to solve for H results in :
H = [PET(t) - RRES
z R(z) K(0) dz +
K(6) dz +
s(z,t) R(z) K(9) dz]/
h(z,t) R(z)
R(z) K(8) dz
(33)
(34)
Equation (34), therefore, allows for the calculation of Hr at
every time step from known values of PET(t), z, R(z) , and K(6).
It was assumed that RRES =1.0 and s(z,t) = 0.0 for the evalua-
tions presented in this report.
24
-------
The soil-water content distributions at selected times
resulting from root uptake, as described by the two models, are
summarized in Table 1. It is apparent that both models pre-
dicted identical uptake patterns up to 4 days, but deviated for
larger times. As illustrated in Figure 4, the potential evapo-
transpiration was met only up to 4 days in the Molz-Remson model,
while in the Nimah-Hanks model "water stress" does not commence
until the 6th day. Recall that the definition of water stress
is different in the two models. In Nimah-Hanks model water
stress is indicated by the approach of Hr to 15-bar value, while
in the Molz-Remson model potential ET cannot be satisfied when
AW/TAW <_Q.2 as defined in equation (27). Therefore, the dif-
ferences in the soil-water content profiles as predicted by the
two models are due to the manner in which the physiological
response of plants to water stress was conceptualized. The
important conclusion, however, is that both Molz-Remson and
Nimah-Hanks models predict identical water uptake patterns as
long as there is no soil water stress. For this reason, the
simpler Molz-Remson model (equation 24 with modifications
described) will be used in our modeling efforts to simulate
water uptake by plant roots.
PLANT UPTAKE OF NITROGEN
Nitrogen uptake by plants involves the movement of water
soluble nitrogen species (NHi* and N03) to roots followed by
their absorption across the root s.urfaces. Mass flow arid
diffusion are the two major processes by which NHi* and NO3 are
transported to the roots . Convective flow of water towards
roots in response to transpiration results in the mass transport
of NHi* and NO3 to the roots along with the soil water. The
concentration of these ions at the root surface decreases when
the rate of root uptake exceeds the rate of supply of these ions
by mass flow. Diffusion of NHi, and NOs towards the roots occurs
due to the concentration gradient.
Arguments abound in the literature as to the relative im-
portance of mass-flow or diffusion as the major process by
which nutrients are supplied to plant roots'*1 fl*7'"*9 '52 . How-
ever, when supply by mass-flow is restricted (such as due to
moisture stress) ,, diffusion becomes a major mechanism of
nutrient supply53"56. Mass-flow may be a dominant process for
nonadsorbed nutrients with high solubilities (e.g. NO3), while
diffusion appears to be significant for adsorbed species (e.g.
P,K,Zn,Fe, etc.). The relative importance of these two processes
will also depend upon the geometry of the root system. Higher
root densities result in shorter distances over which ions must
be transported; hence, diffusion may be responsible for the
transport of a considerable amount of a given nutrient to the
root surface.
25
-------
TABLE 1. COMPARISON BETWEEN SOIL-WATER CONTENT (9) PROFILES DURING AN 8-DAY PERIOD
IN A SANDY SOIL AS SIMULATED USING THE MOLZ-REMSON (M-R) AND THE NIMAH-HANKS
(N-H) MODELS FOR PLANT UPTAKE OF SOIL WATER.
to
Soil
Depth
(cm)
10
20
30
40
50
60
70
80
90
2 Days
M-R
0.0638
0.0621
0.0623
0.0633
0.0651
0.0674
0.0702
0.0734
0.0769
N-H
0.0638
0.0622 "
0.0624
0.0634
0.0651
0.0673
0.0701
0.0733
0.0768
4 Days
M-R
0.0513
0.0500
0.0502
0.0510
0.0523
0.0542
0.0568
0.0604
0.0660
N-H
0.0513
0.0501
0.0502
0.0510
0.0524
0.0542
0.0568
0.0603
0.0660
6 Days
M-R
0.0405
0.0396
0.0397
0.0402
0.0412
0.0424
0.0442
0.0466
0.0506
N-H
0.0448
0.0438
0.0439
0.0445
0.0456
0.0471
0.0491
0.0521
0.0569
8 Days
M-R
0.0319
0.0314
0.0314
0.0318
0.0324
0.0333
0.0344
0.0360
0.0386
N-H
0.0427
0.0418
0.0419
0.0425
0.0435
0.0448
0.0467
0.0494
0.0539
-------
Due to the uncertainties in the mechanisms of nutrient
transfer across root surfaces, several models have been pro-
posed. These models may be classified into two groups. In the
first group, the rate of solute uptake is assumed to proceed
at such a rate as to maintain either a constant or zero solute
concentration at the root surface1*8'58. In the second group of
models, the solute flux into the roots is assumed constant or
varies linearly or nonlinearly with solute concentration at the
root surface"5"*7'1*9'58'61-63. The nitrogen species taken up
by plant roots are NH^ and NO3. However, due to the relatively
rapid transformation of NIU to N03 and the greater'mobility of
the latter ion, most researchers have considered only the up-
take of NO3 by plants.
From a sensitivity analysis of a nutrient uptake model that
accounted for diffusive-convective flow to roots, van Keulen et
1.O
0.8
LU
Q. 0.6
0.4
O.2
4567
Tl M E, D A Y S
8
Figure 4. Evapotranspiration (ET) as a fraction of potential
evapotranspiration (PET) with time as simulated
by the Molz-Remson (M-R) and the Nimah-Hanks (N-H)
models.
27
-------
al.6" concluded that virtually the whole nutrient supply in the
root zone may be available in a short time to an actively grow
ing root system. They suggested that root density played a
significant role in determining plant nutrient uptake. Russell
and Shone65 demonstrated that when part of the intact root sys-
tem of barley was exposed to more favorable conditions (higher
nitrogen concentrations) than the remainder, root proliferation
was limited exclusively to that zone with favorable conditions.
Thus, higher root densities should result in a greater nutrient
uptake by the root segments in the favorable environment. 66
Similar conclusions were arrived at by Jungk and Barber ' from
a series of experiments where root trimming and/or split-root
techniques were utilized to investigate nutrient uptake by
plant roots. Brower and de Wit67, however, have also observed
root density increases when nutrients were limited. Our under-
standing of the physiology of the plant root systems regarding
compensatory growth and uptake under conditions of nutrient
and/or water stress is inadequate. The concentration of nutrients
and root density (number, length, area, etc.) in a given soil
volume appear to be important to plant root uptake. The trans-
port of nutrients to root surfaces is not likely to be a
limiting process as long as the root density is high.
It must be recognized that in all of the nitrogen uptake
models discussed in the preceeding paragraphs, transport of
water and solutes only in the radial direction towards the roots
is considered; losses or gains of water and solutes within a
unit volume soil element due to vertically upward or downward
flow are ignored. Thus, the nutrient uptake models currently
available treat the soil profile as being "static" with regard
to vertical flow. A comprehensive three-dimensional treatment
of water and solute flow to describe plant uptake is not avail-
able at the present time.
In light of the above discussion, the microscopic pro-
cesses (diffusion and mass flow) responsible for transporting
nitrogen to the root surfaces were ignored in this study and the
uptake of nitrogen was modeled as a sink term in the flow equa-
tions. The rate of nitrogen uptake (q™ax) was calculated as
follows: N
max _max
qN = QN
R(z,t)dz (35)
o
IT13X
where, QN represents the nitrogen uptake demand (ygN/day/cm2
soil surface) of the crop under non-limiting nitrogen supply;
the integral of the root length distribution, R(z,t), over the
rooting depth L yields the total root length (cm root/cm2 soil
surface); and q$ax has the dimensions of yg N/day/cm root. The
values of Qg were determined by analyzing experimental data
for cumulative nitrogen uptake during the season for a specific
28
-------
crop (in our case corn) grown under nonlimiting water and nitro-
gen conditions. This approach is similar to that used by Watts63.
Empirical models were also developed (to be discussed later)
using experimental data to simulate the root length distributions,
R(z,t), in the soil profile at various times during the growing
season.
In deriving equation (35), it was assumed that the root
capacity for nitrogen absorption was uniform over the entire
root system. Thus, root length distributions represented the
"sink strength" for nitrogen uptake. However, the root absorp-
tion capacity is known to be neither constant nor uniform, but
influenced by several factors62'66'69-71 (e.g. root diameter,
age, and distance from stem base). Based upon the work of Dibb
and Welch72, the uptake of both N03 and NH^ species was con-
sidered. Data are presently unavailable to determine the
fractional uptake of NH4 and N03 when both species are present.
The actual rate of nitrogen uptake (q ) was determined by a
Michaelis-Menton type relationship based on the total concen-
tration of NHit and NO3 species in the soil solution:
_ max rA
(z,t) + B(z,t) ,
+ A(z,t) + B(z,t) J
(36)
where, A and B are solution concentrations of NH4 and N03; Km
is the value of (A+B) when q^ = 0.5qjjax. Total nitrogen uptake
demand (qjj) was satisfied by uptake of both NHij and N03 as
follows:
q,T = q, + q~ (37)
max
max
A(z,t)
A(z,t) + B(z,t)
B(z,t)
A(z,t) + B(z,t)
-]
(38)
(39)
where, qA and q
B
are rate of uptake of
and NOs/ respectively,
and other parameters are as defined previously. The value of
q and q when multiplied by the R(z,t) in a given volume element
£\ O
of the soil profile yields the value for the corresponding up-
take sink term in equations (12) and (13) . Thus the total
amount of nitrogen extracted from the root zone within a time
increment At may be calculated as:
q R(z,t) dtdz +
'qDR(z,t) dtdz
~D
(40).
29
-------
where U is cumulative amount (UgN) of nitrogen (NH4+NO3) taken
up from the root zone during the time increment At=t2-ti; other
parameters were defined previously.
In summary, in our uptake model the amount of nitrogen
taken up by the plants is dependent upon (i) the nitrogen re-
quirements of the plant (QmaX), (ii) the root length distribu-
tions [R(z,t)l, and (iii) the concentration distributions of N
and NO3 within the root zone. Transport of nitrogen species to
the root surfaces is implicitly ignored in our model.
ROOT GROWTH MODELS
Utilization of the models for water and nitrogen uptake,
described in earlier sections, requires a knowledge of the
exact nature of the root distribution in the soil profile at all
times during the growing season. Reliable experimental tech-
niques to measure root distribution are currently being eval-
uated73 . However, measuring root lengths and numbers by the
"line intersect" method7" appears to be the most popular pro-
cedure.
Our understanding of the dynamics of root growth is sparse.
Limited quantitative data do not permit formulation and/or ver-
ification of conceptual root growth models. Several researchers
have investigated the influence of various soil and crop factors
on root development. Some of the more important soil physical-
chemical properties regulating root growth are: soil bulk den-
sity75, porosity75, soil-water suction75, pH76 and aluminum
content . Rooting habits (such as shallow or deep rooted) as
well as sensitivity to the above listed soil parameters are not
only different for individual crops but also vary from variety
to variety for the same crop.
Root growth may be considered to consist of concurrent
processes of proliferation, extension, senescence and death77.
Localized increase in root density due to branching without an
increase in the total volume of root zone is refered to as pro-
liferation. Extension is the process by which the root system
penetrates to deeper depths. Suberization and gradual reduc-
tion in root permeability is termed senescence. Further aging
leads to eventual death of the roots. .Following Hillel and
Talpaz77 the length of active roots, R!, at depth i and time j
may be expressed as:
RJ = RJ'1 + R?'1 P At - R^"1 D At + R^"1 E At (41)
where, R?~ is root density (cm root/cm3 x soil) at the same
depth at a previous time j-1 (At time units earlier); P is
proliferation rate, D is death rate and E is rate of extension,
30
-------
Ri_l is root length in the previous (j-1) time step in the
overlaying depth increment (i-1) . Note that P, D, and E are
rates per unit time expressed as a fraction of the existing
root length. The process of senescence is disregarded in equa-
tion (41). Thus, the use of Hillel-Talpaz77 model would require
a knowledge of at least three growth parameters (P, D, and E) .
Lambert et al.78 presented a conceptual model to describe the
development of two-dimensional root systems. Their model
accounted for (i) the effect of soil-water suction (or water
content) on rate of root growth at any position in the soil
profile, and (ii) the concept of geotropism of roots, i.e.
preference for downward rather than horizontal growth. Whisler79
modified this model to include impedence of root growth result-
ing from soil layering.
The general problems in development and testing of models
for root growth were summarized by Hillel and Talpaz77 as
follows :
11 .......... the very ease with which
theoretical models can be developed
into increasingly complex hypothetical
constructions without any apparent
logical limits presents a problem in
itself. The imagination of modelers
and the capability of computers
already exceed the bounds of our
experimental information on the
behavior of the real system which we
may pretend to simulate. However
much we believe our own model to be
based on essentially sound concepts
of soil moisture and root system
dynamics, it still requires rigorous
testing, which is indeed a very
arduous and painstaking task."
Because of these problems, empirical models were devised
to simulate root length distributions on the basis of experi-
mental data of NaNagara et al.63 for corn (Zea mays L.) grown
under field conditions on Maury soil. Empirical equations were
obtained by "curve fitting" to measured distributions at
selected times during the season. These equations are as
follows:
R*(z,t) = [R* 1 [exp(-Bz)] tcos()] (42)
Illcl2C A.AJ
where, R*(z,t) = root length density (cm root/plant/cm depth)
R* = maximum root length density (at soil surface, z=0) ,
max
31
-------
z = soil depth (cm)
L = depth to the bottom of root zone (cm)
The values of the parameters R*ax, L, and 3 in equation (42)
varied during the growing season as follows:
n ; N<5
max
L =
(43)
(-0.05253N2 + 24.26667N - 120); N>5
(0.06N2 - 0.1N)
N<29
(44)
(-0-0112N2 + 2.53N - 15.0); N>29
0 ln[2 cos (TTZ, /0/2L)
P — -i-/ &
where,
'1/2
(45)
L[-0.0001854N2 + 0.022N - 0.102]
(0.4) (L) ; z1/2< 0.4L
(46)
and represents the soil depth at which root length density is
one-half the value of R* and N is the number of days since
max
planting. Note that the values of R*(z,t) are expressed as
cm root/plant/depth. The effect of crop planting density (PD,
plants/cm2 surface) must be known prior to using the uptake
models. For the case of 48,000 plants/ha, PD = 4.8 x 10"** plants/
cm
soil surface -and the adjusted root density (cm root/cm soil
surface/cm depth) is:
R(z,t) = R*(z,t) x 4.8 x 10'
(47)
Root length distributions calculated at selected times using
these empirical equations are presented in Figure 5. Increases
in root length density at all depths and deeper penetration of
the soil profile by the root system with time is evident.
In adapting these root distributions for inclusion in the
uptake models, it was assumed that root absorption capacity for
water and nitrogen was uniform and remained constant during the
growing season over the entire root system. We recognize that
32
-------
the empirical model presented here is not adequate for a general
model. However, in the absence of a better understanding of root
growth dynamics and the unavailability of input parameters for
the conceptual models, the empirical models may satisfy our
present needs.
CM. ROOT/CM3/PLANT
0 20 4O
E
u
a.
UJ
Q
O
to
Simulated Root
Growth
1OO
Figure 5. Root length density distributions for corn (Zea
mays L.) at selected times during the growth
season as calculated by the empirical model.
33
-------
SECTION 6
MANAGEMENT MODEL
The research model, described in Section 4, is conceptually
pleasing in that it provides a mechanistic description of the
soil-water-plant system. This model, and others like it, re-
quire an extensive number of parameters, many of which are
generally unavailable. Also, application and verification of
these models for large watersheds becomes difficult owing to
the spatial variability of input parameters for soil/plant
properties. However, research models such as that presented
in Section 4 are useful in performing sensitivity analyses to
identify the most significant processes and/or parameters,
thereby allowing simplifications in the model. Simpler models
become desirable when only gross descriptions are required. A
simple conceptual management-type model for describing the fate
of nitrogen in the plant root zone is presented in this section.
TRANSPORT OF WATER AND NITROGEN
Several simplified forms of the transient, one-dimensional
water flow model (equation 1) have been used1 "*' 2 8' 8 °. Perhaps
the most simplified concept is that of "piston displacement"
used by Frere et al.81 and Rao et al.82. The conceptual methods
proposed by these latter authors are discussed in detail here.
The technique is based on two principal assumptions: (i) all
soil pore sequences participate in solute and water transport,
and (ii) the soil water initially present in the profile is
displaced ahead of the water entering at the soil surface.
Consider the infiltration of an amount of water, I, into
a homogeneous soil profile, with a uniform initial soil-water
content fraction of 61 (cm3/cm3). The depth to which the
wetting front will advance can be calculated from:
dwf ' H^TT ' 9f>6i H8)
where, dwf is the distance (cm) from the soil surface to the
wetting front, and 0f is soil water content in the wetted zone
behind the wetting front. For infiltration of 5 and 10 cm of
water into an initially dry (8i=0) soil, the wetting front depth
(dwf) would be 14.3 and 28.6 cm, respectively, when 9f=0.35 cm3/
34
-------
cm3 (Figure 6). However, if Qj_ was 0.10 cm3/cm3 and 9f was
0.35 cirr/cm3, the wetting front would be at 20 and 40 cm, re-
spectively, for the 5 and 10 cm water applications (Figure 7).
Therefore, for a given water application and 0f, the wetting
front depth increases as 9i increases.
If assumptions (i) and (ii) given above are valid, then
the water at the observed wetting front for 6i>0 is the water
initially contained in the soil profile and not that added at
the soil surface. Hence, complete displacement of the initial
water (9i>0) results in a nonadsorbed solute front being lo-
cated at:
dsf =
(49)
Soil-Water Content
o.o 0.2 0.4
Concentration t
Figure 6. Distribution of soil-water (solid line) and non-
adsorbed solute (dashed line) after 5 and 10 cm
of water had infiltrated into an initially dry
(9.=0),soil profile.
35
-------
where dsf is the solute front position (cm). Dividing equation
(49) by equation (48) and rearranging terms yields:
sf
= n - —
[ ef
(50)
Note that the value of the ratio (dsf/dwf) is equal to 1.0
when 9i=0 (i.e., infiltration into oven-dry soil); thus the non-
adsorbed solute front rides on the wetting front. However, when
0i>0 (i.e., infiltration into moist soil), the nonadsorbed solute
front would lag behind the observed wetting front [(dsf/dwf)<1].
Equation (50) is not valid for the case of Q±=Qf, as the ratio
(dsf/dwf) is equal to zero. Note that the nonadsorbed solute
front position depends on the amount of water added and the
average soil-water content in the wetted zone behind the wetting
front, but not on the initial water content (Figures 6 and 7) .
Soil-Water Content
40 80
Concentration,
Figure 7. Distribution of soil-water (solid line) and non-
adsorbed solute (dashed line) after 5 and 10 cm
of water had infiltrated into a soil profile at
a uniform initial water content (6^, shown as
vertical dashed line) of 0.1 cm3/cm3.
36
-------
This conclusion is in agreement with experimental observations
of previous workers82"85.
Published data for NOT and Cl~ movement in several soils
were used to test the validity of assumptions (i) and (ii).
These data are presented in Figure 8 and are compared to equa-
tion (50). Considering the wide range in experimental conditions
and that both laboratory and field data were included, the agree-
ment between the 1:1 line and the data is excellent. Apparently,
in all the cases considered, the initial soil water in the pro-
file was displaced .ahead of the applied water; thus, supporting
our, principal assumptions.
At the termination of infiltration, the soil water content
in the wetted zone decreases due to drainage or redistribution
until the profile attains a "field capacity" water content (8pc)•
The movement of the solute front due to this process is deter-
mined by the amount of "drainable" water above the depth dsf.
9 Balasubramanian, 1974
D Cassel, 1971
O Ghuman et al., 1975
• Kirda et al., 1973
A Warrick et al., 1971
Fiqure 8. Agreement between dsf/dwf and &±/Qf as calculated
by Equation (50) and experimental data from
various sources.
37
-------
It can be shown that:
(d ,;) (A9)
d' = d - + s% '(51)
sf sf epc
where dsf is solute front location after redistribution, A9=
(8f-6FC), and the product (dsf)(A6) represents the amount of
"drainable" water above dsf. Substitution of equation (49) for
dsf in equation (51) yields:
d' = T±- (52)
Sf 6FC
The validity of equation (52) is limited to the case where the
solute front is initially located at the soil surface (z=0)
prior to infiltration. For a case when the solute front is
located at some depth di (di>0) before infiltration, equation
(52) must be modified to:
d' = d. + yL_ (53)
sf i .9FC
The mobility or depth to which an adsorbed solute front
penetrates is reduced due to adsorption-desorption processes.
By assuming a linear and reversible equilibrium adsorption model,
a retardation factor (R) can be calculated,
PK
R = 1 + o-^- (54)
9FC
where, p is soil bulk density (g/cm3), KD is adsorption parti-
tion coefficient (cm3/g), and 9pc is field capacity water con-
tent (cm3/cm3). Equation (53) can be generalized to predict
reactive front locations for adsorbed solutes:
dsf - fli + 5 ^ <55)
where, R is defined by equation (54). For a nonadsorbed solute
(KD=O) the retardation factor R equals one, and equation (55)
reduces to equation (53). Note that dsf for a previous event
becomes di for the next event.
Many practical solute transport problems occur in the
presence of a growing crop. Extraction of water from the root
zone results in a nonuniform soil-water content profile. Thus
modifications must be made in the equations derived so far to
account for this case. By assuming a "static" soil profile
(i.e., the vertical flow of water stops after &„„ is attained),
£ \*>
38
-------
equation (23) may be reduced to equation (30), which is repeated
here: ^
J\ O
= -W(9fZ,t)
where, the Molz-Rerason37 model (equation 24) was used to describe
the uptake of soil water by roots.
Depletion of water by plant roots creates a soil-water
deficit in the profile. The deficit (I^) above the solute front,
is:
zd ~
dsf
o
[epc - e(z)j dz (56)
where, the water content profile 8(z) is predicted by equation
(30) at any time, and dsf is defined by equation (55). The
deficit (Id) must be satisfied by an input (I) from an irrigation/
rainfall event before movement of the solute front can occur.
Thus, the effective amount of water (Ie) for moving the solute
front is:
Ie = I - Id (57)
For the case when the deficit is overcome by an event (i.e.,
Ie > 0) , the new location of the solute front may be calculated
from:
d = d. + e • -, I > 0 (58)
However, for the case when the event is not large enough to over-
come the deficit (i.e., Ie<0), there is no movement of the solute
front:
d f = d., Ie£0 (59)
The input water, after adjusting for the evapotranspiration loss,
during the redistribution period (assumed to be two days), was
distributed in the soil profile to a depth dx by successive
iterations to satisfy the following conditions:
(I - 2ET) =
"X[9_r-e(z)]dz, dxldsf (60)
o FC
39
-------
where, ET is the evapotranspiration demand (cm/day). All cal-
culations involving root extraction were performed on an IBM
360/370 digital computer.(FORTRAN IV program).
Leaching of a chloride pulse through a Eustis (Typic
Quartzipsamment) fine sand field profile, with a fully
established crop of millet [Pennisetum americanum (L.) K. Schum],
was measured89 during a 60-day period between August 1-September
24, 1973, at Gainesville, Florida. Chloride data was used to
verify the present model. Experimentally measured90 soil
hydraulic conductivity versus soil-water content for the same
field plot was fitted to the following relationship:
K(0) = Exp [B9a + D] (61)
with B = -3.3471, a = -0.62, and D = 10.1753. The effective
root absorption function, R(z) was assumed to be:
R(z) = Exp [-O.OOSz] - 0.471 (62)
where, z is soil profile depth. Equation (62) describes an
exponential decay root absorption function, where 39, 28, 19,
11, and 3% of the total root activity was present in each
successive 30-cm segment of the soil profile to 150 cm. This
empirical equation was developed to describe a fully established
root system and was based on observed root density distributions
for this crop. The potential evapotranspiration demand (PET)
was assumed to remain constant at 0.3 cm/day during the 60-day
simulation period. The rainfall distribution at the experimental
site was also recorded89 and used as input for the present model.
The Eustis soil profile drains to a field capacity (6pc) of
0.08 cm3/cm3 two days after any input event. Plant available
water was defined to be that held in the profile between field
capacity (6pc) an& 15-bar (615=0.03) soil-water contents*.
Experimentally measured89 field data for chloride front
location and that estimated by the present model are compared in
Figure 9. Considering all the simplifying assumptions in the
model, the agreement between measured and predicted values is
good; thus, verifying the model for predicting solute front
position in a field soil profile in the presence of a crop. The
success of this simple model led to further improvements to
incorporate microbial transformations and plant uptake of nitro-
gen. These modifications are discussed in the following
sections.
NITROGEN TRANSFORMATIONS
The partial differential equation describing the simul-
taneous transport and transformation of nitrogen species is:
40
-------
37
(63)
where, 3(9Ci)/3t is change in the mass of the i nitrogen species
with time, (-3q/8z) is the net change mass due to transport pro-
cesses (diffusion + mass flow) , i represents production or loss
of mass due to transformations of the ith species. Expanded
versions of equation (63) for transformations during transient
one-dimensional flow are given in Section 4 (see Equations 12-15).
Because analytical solutions to these non-linear partial dif-
ferential equations were unavailable, numerical solution
techniques were employed to solve them.
The more complex model can be simplified, however, to a set
of simple first-order kinetic equations if the total amounts
[Ti(t)l of a given nitrogen species in the profile are considered
10
20
30 40
TIME, days
50
Figure 9.
Comparison between measured (solid circles) and
predicted (solid lines) position of a nonadsorbed
solute front in a sandy soil at various times.
The soil was planted to millet. [Pennisetum
americanum (L.) K. Schum]
41
-------
rather than actual concentration distributions Ci(z,t)
total amounts in the root zone are defined as follows:
TI = /" Ci dz
T2 = / 6C2 dz
T3 = / 9C3 dz
The
-00
dz
(64)
(65)
(66)
(67)
.th
where, Ci represents the concentration distribution of the i
species in the soil profile, p is the bulk density, 0 is the
volumetric soil water content, and the subscripts 1, 2, 3, 4
refer to exchangeable NEU , solution-phase NEU / solution-phase
NO3, and organic-N, respectively. First-order kinetic trans-
formations considered in the present case were (i) equilibrium,
reversible ion-exchange of NEU, (ii) immobilization and nitri-
fication of NEU, and (iii) mineralization of organic-N. Immo-
bilization of NO3 is relatively less important than that of
NEU in most situations; hence, this process was not considered
in the management model. Furthermore, by assuming deep well-
drained soil profiles, the process of denitrification was not
included in the analysis presented in this section.
Expansion of equation (63) to include the transformations
described above for NO3 gives:
-gr ^ + ki6C2 (68)
o u. o Z
Integration of equation (68) over the soil depth (z) yields:
_
at
ec3 dz =
J- If
dZ
dz
(69)
By assuming the transformation rate coefficient ki to be inde-
pendent of soil depth, recalling the definitions of equations
(65) and (66), and integration of equation (69) gives:
dT
3 _
dt
= Aq + kiT2
(70)
where, (dT3/dt) is the change in the total mass of N03 in the
profile with time, Aq is net solute flux, ki is kinetic rate for
nitrification, and T2 is total amount of solution-phase NEU in
the profile. Equation (70) can be simplified further by
assuming the net flux to be zero (i.e. Aq=0). This assumption
42
-------
can be satisfied in two ways: (i) if influx is equal to out-
flux, or (11) when both influx and outflux are zero. We chose
the latter condition, such that no solute was added to or left
the profile for a specific time period. Thus, equation (70)
reduces to a simple first-order rate equation as follows:
(71)
The simplification techniques described above were applied
to the equations for other nitrogen species:
dt
T2 + k9T,,
(72)
(73)
(74)
where, T± and k^ are as defined previously, K is partition co-
efficient relating total mass of
that in the adsorbed-phase.
in the solution-phase to
Two major assumptions involved in the derivation of equa-
tions (65) through (68) are: (i) the soil profile is homo-
geneous in that kinetic_rate coefficients (ki) and adsorption
partition coefficient (K) are constant with depth, and (ii) the
net solute flux (Aq) is zero and/or inflow and outflow of solute
are zero within the region of interest. Subject to these
assumption and when the initial total amounts (Ti°) of each
nitrogen species in the profile are known, the analytical so-
lutions to equations (71) through (74) are as follows (Rao et
al.81*):
[l-exp(B2t)l
Ti = KT2
T2 = A exp(3it) + B exp(3at)
T3 = To3 _ |iA [1_exp(B1t)] -
Ti» = C exp($it) + D exp(3at)
where ,
23! = -(ki., + k3) + [(kU - k3)2 + 4kltk$]1/2
232 = -(kU + k3) - [(kU - k3)2 + 4kltk|]1/2
(75)
(76)
(77)
(78)
(79)
(80)
43
-------
ki\ = (k! + kO/d + K) (8D
k§ = k3/(l + K) (82)
a _ kjTg - Tg(kU + B2) (83)
(0i - 62)
B = T? - A (84)
- Tg (k3 + B2)
D = TS - C (86)
also, T° and k. are as defined previously.
The total amounts of each nitrogen species calculated using
equations (75) through (86) were in agreement with those ob-
tained with numerical solutions to the model for transport-
transformations'* under steady-state water flow. Results from
these analytical solutions, when reduced for limited trans-
formations (adsorption and nitrification of NHi* only) , agreed
well with results obtained from the model presented by Cho92.
A sensitivity analysis of the transformation submodel has been
performed by Rao et al.91 using these analytical solutions.
Since the management model was devised to evaluate the
gross behavior of nitrogen in the root zone, the analytical
solutions described here were utilized to describe micro-
biological transformations.
NITROGEN UPTAKE
Empirical Michaelis-Menton type equations were used to
calculate nitrogen uptake by a growing root system. These
equations related the nitrogen uptake rate (Q ) to total amount
(TN) of mineral-N (NIU + N03) in the soil solution withinThe
root zone:
T
^ _max , N
Q = Q
N N KM A T
M + N
where, KM is the value of TN when Qjsj = 0.5Q§ax. Recall that
gmax represents the N-uptake demand (yg N/day/cm2 soil surface)
under "ideal" growth conditions. The actual uptake demand (QN)
was assumed to be satisfied by absorption of both N03 and NH^
in proportion to their respective total quantity in the soil
solution in the root zone as follows:
QN = Qa + Q3 (88)
44
-------
01 - Q ''
03 - Q <>
where Q2 and Q3 are uptake demand for NH^ and N03, respectively,
while T2 and T3 are total amounts of NH4 and N03 in the soil
solution-phase in the root zone.
The. values of QN X were obtained in a manner similar to
that described in Section 5. The empirical root growth model,
also described in Section 5, was used to calculate the root
length density distribution in the soil profile, and to esti-
mate the soil depth (L) to which roots had penetrated. The
value of L was then used as the upper limit of integration in
equations (64) through (67) in calculating the values of T2 and
T3 in equations (88) and (89) .
Application of the management model is limited to homo-
geneous soil profiles. Furthermore, the model is applicable
only to deep, well-drained soil profiles due to assumptions
made in the nitrogen transformation submodel. Finally, the
management model presented here allows for estimation of the
solute front position and the total amount of solute in the
root zone, but does not permit calculation of solute concen-
tration distributions within the soil profile.
45
-------
SECTION 7
RESEARCH MODEL SIMULATIONS
In this section, the research model was used to provide
simulated results for selected cases in order to describe the
fate of applied nitrogen in the plant root zone. The values
for the model parameters were chosen to represent some real
systems and were based on published data.
TRANSPORT AND TRANSFORMATIONS
Simultaneous microbiological nitrogen transformations
during transient unsaturated flow were described using equations
(1) and (12) through (15). The root extraction of soil water in
response to transpiration and plant uptake of nitrogen (Section
5) were not considered. In order to illustrate the importance
of the transformation mechanisms and their dependence on soil
water conditions, two cases were simulated. The first case
was for transport and transformation of an applied NHi^NOa pulse
in a uniform well-drained soil profile. The second case rep-
resents a soil profile with an impermeable barrier.
For both cases presented here, the soil parameters used
represent a loamy soil profile. The initial soil water content
(0i) was uniform at 0.1 cm3/cm3 throughout the profile. The
soil profile was assumed void of initial mineral (NHit+NOa)
nitrogen, while the "mineralizable" organic-N distribution at
t=0 was described by:
OM(z) = 50.0 [exp(-0.025z)] (91)
where, the maximum "mineralizable" organic-N content of 50ug N/
gm was at the soil surface (z=0) and decreased exponentially
with depth. It was assumed that NEUNOs fertilizer was applied
at the soil surface followed by infiltration of water for a
period of 12 hours. It was further assumed that the applied
NH^NOa fertilizer was dissolved by the infiltrating water and
entered the soil within 2 hours, resulting in an input solution
concentration of lOOyg N/ml for both NE^ and N03. The soil
surface was assumed to be maintained saturated (9z=0 = 6saj- =
0.36 cm3/cm3) during infiltration. The total amounts of nitro-
gen and water applied in this manner were 348 ygN/cm2soil sur-
face and 9.1 cm of water, respectively. Evaporation at the soil
46
-------
surface was assumed constant at 0.3 cm/day during the redistri-
bution period (t>12 hours).
The soil water content distribution in a deep uniform soil
profile at selected times during water infiltration and redis-
tribution is shown in Figure 10. At the termination of infil-
tration (12 hours), the wetting front had advanced to a depth
of 36 cm. Given the nearly uniform soil water content of 0.36
cm3/cm3 in the wetted zone, the depth of wetting front (dwf)
can be calculated by equation (48) as 9.I/(0.36-0.1) = 35 cm.
WATER CONTENT .,cm3/cm3
O O.1O 0.20 0,30 040 0.50
Figure 10,
Simulated soil-water content distributions in a
deep uniform loam soil profile during infiltration
and redistribution of soil-water
47
-------
During water redistribution, the wetting front advanced to
lower depths as a result of drainage from the wetted zone.
After 14 days, the wetting front was located at about the 56 cm
depth, and the soil-water content in the wetted zone was approxi-
mately 0.21 cm3/cm3. Depletion of water due to evaporation re-
sulted in decreased water contents close to the soil surface
(Figure 10).
The solution-phase concentration distributions of NHU and
NO3 during infiltration and redistribution of water in a uni-
form soil profile are presented in Figure 11. _The transforma_-
tion rate coefficients chosen were ki = 0.01, k2 = 0.00001, k3
= kit = k5 = 0.0001 hr"1, and the adsorption coefficient (Ko)for
NH^ adsorption was 0.1 cm3/g- The magnitude of the transforma-
tion rate coefficients used in the simulations are within the
range of values reported in the literature and given in Table
3 in Appendix D (Stanford and Smith16; Stanford and Epstein25;
Stanford et al.87; Miller and Johnson24).
CONCENTRATIONS, pg-N/cnrr3
E
0
I
UJ
Q
O
20 40 60 80 ^0 20 40 60 80
20 40 60 80 <3 20 40 60 80
Figure 11.
Simulated solution-phase concentration distribu-
tions of N03-N and NHi,-N in a deep uniform loam
soil profile during infiltration and redistribu-
tion of soil-water. The rate coefficient for
nitrification (ki) was 0.01 hr"1.
48
-------
The position of the N03-N front at the termination of water
infiltration (t=12 hrs) is at 25 cm and can be calculated by
equation (37) with I = 9.1 and 9f = 0.36. The NH* pulse front
is at about 17 cm and lags behind the N03 pulse due to adsorp-
tion. Additional movement of the NHi, and N03 pulses during
redistribution is small (Figure 11). However, the N03 concen-
tration profiles show double peaks for times between 2 and 6
days. The position of the smaller peak coincides with the lo-
cation of the NHi> peak. The presence of the second peak on the
N03 pulse is thus attributed to N03 generated by nitrification
of NHi* during redistribution. For greater times (t>6 days) ,
the second peak disappears and the N03 concentration profile
becomes broad and asymmetrical. A gradual decrease in the area
under the NHi* pulse is associated with a simultaneous increase
in area under the N03 pulse due to nitrification. The effect
of the nitrification_rate coefficient (ki) is clearly illustrated
in Figure 12, where ki was 0.1 hr""1. Note that within 6 days
more than 90% of NH^ disappeared from the soil solution.
NH4& NO3 CONCENTRATIONS, pg-N/cm3
2O 40 60 80 JD 2O 4O 6O 8O
E
o
CL
LU
Q
u
10
20
30
40
•
^ _NH4 •
^=~~S_
^> *• — ** Ti i^^
., " NOs
X
/
12hr
U
10
20
30
40
i
V
N^^
) ^~~~^>
f 'x '
s
„**'
^ ^
*»^
^^^
s+~~
/
6 days .
>>ii
.0 20 40 60 80 _O 2O 4O 6O 8O
0
10
2O
3O
4O
• i i •
>.__
""*5
'--
_^>
• ^ -•"""""
2 days .
a • • *
u
10
20
30
40
V
\
\
"**^^
^^^
~~-^
N
/
^--"
f 14 days .
Figure 12.
Simulated solution-phase concentration distribu-
tions of N03-N and NHi,-N in a deep uniform loam
soil profile during infiltration and redistribu-
tion of soil-water. The rate coefficient for
nitrification (ki) was 0.1 hr"1.
49
-------
The total amounts of NO3 and NIU (adsorbed + solution)
present in the soil profile versus time for the cases where
k~i = 0.01 or 0.1 hr'1 are shown in Figure 13. Nearly_all Ntt.* ^
was transformed within 4 days after application when ki- 0.1 hr
while significant amounts of NHi, remained in the profile when
ki = 0.01 hr"1. The decreases in amount of NHi* are nearly equal
to the increases in NO3. The total amount of organic-N mineral-
ized within the soil profile during the 14-day period was 75
pg N/cm2 for ki = 0.01 hr-1 and 76 yg N for ki = 0.1 hr~ . For
both cases, however, the amount of nitrate lost due to denitri-
fication was negligible (0.35 yg N) because the soil-water
contents were not favorable for denitrification (see equations
lOa and lOb) during the simulated period.
400
350
o> 300
Q 250
06
200
< 150
O
•- 100
50
0
-1
K1=0.1 hr
= 0.01
4 6 8. 10 12 14
TIME, days
Figure 13.
0
Total amounts of NHit-M and NOs-N in a deep uni-
form loam soil profile during infiltration and
redistribution of soil-water^ The nitrification
rate (ki) was 0.01 or 0.1 hr 1. These plots were
derived from the simulated data presented in
Figures 11 and 12.
50
-------
The influence of an impermeable barrier at a depth of 40 cm
in the soil profile is illustrated in Figure 14. The presence
, of a1 barrier resulted in higher soil-water contents at all
depths during redistribution in comparison to a uniform well
drained profile. Higher soil-water contents favor the denitri-
fication of N03 as evidenced by the data presented in Figures
JL5 and 16. _The transformation^rate coefficients chosen were:
ki = 0.01, k2 = 0.00001, k3 = k4 = 0.0001, and k5 = 0.01 hr"1.
Losses of NO3 due to denitrification during the early periods
of redistribution (12 hrs
-------
pulse) had also decreased. However, for longer times (6 and
14 days), lower soil water contents were more favorable for
nitrification than for denitrification. Thus, NO3 began to
accumulate in the soil profile (Figure 15). The effect of the
magnitude of the denitrification rate coefficient are summarized
in Figure 16. For k5 = 0.001 hr"1 and 0.01 hr"1, the total
amount of NO3 decreased and N-released increased up to 4 days.
After this time, there was only a small amount of N released,
while the total amount of NO 3 increased rapidly due to nitri-
fication.
TRANSPORT, TRANSFORMATIONS, AND UPTAKE
The simulations presented in the previous section did not
include plant uptake processes. In this section, simulations of
Q_
UJ
Q
_J
o
i/>
NH4& NO3 CONCENTRATIONS, pg-N/cm3
0
10
20
30
4O-
0 20 40 60 80 ,£>
^- N03
12 hr
10
20
30
4O
20 40 6O 80
6 days
o(
10
20
30
40
3 20 40 60 80
i i • >
\ "" ' .^
V i— ^**^
^^-^"^n^
^ ^
. x"
/
>
2 days -
rf
10
20
30
40
2O 40 6O 8O
. , .
\ \
\ X
\ xx
N \
)
/ S
/
' s
s
s
s
s
/
/
\
14 days •
Figure 15.
Simulated solution-phase concentration distri-
butions of NH^-N and NOs-N during infiltration
and redistribution of soil-water in a loam soil
profile with an impermeable barrier at 40 cm
depth. The kinetic rate coefficient for deni-
trification (ki) was 0.01 hr"1.
52
-------
nitrogen behavior in the plant root zone are described using the
complete research model. Thus, the major processes of simul-
taneous transport, transformations and plant uptake were con-
sidered. The soil parameters used in these simulations are
similar to those used in the previous section. The plant
parameters are for a corn crop and are based on experimental
data of NaNagara et al.63. The simulations presented here
commenced 34 days after plahting and proceeded 83 days into
the crop growing season. This 7-week period was chosen since
it was the most active in terms of crop demand for nitrogen and
water.
The initial soil-water content (6i) on the 34th day was
assumed uniform at 0.1 cm3/cm3 over the entire crop root zone
(0-90 cm) , and the soil profile was assumed initially devoid of
D)
25O
200
150
^ 10O
P 50
-------
any mineral nitrogen. The mineralizable organic-N distribution
was described by equation (91) with a total of 2863 yg of
organJ.c-N/cm2 in_the root zone_^ The kinetic rate coefficients
were ka = 0.01, k2 = 0.00001, k3 = k4_= 0.0001 hr-1, while losses
due to denitrification were ignored (ks = 0.0). The adsorption
coefficient for NIU was 0.1 cm3/g-
At day 34 of the growing season, NH^NOs fertilizer was
applied at the surface and was followed by two 9.1 cm water
application which requires 12 hours. The soil surface was
maintained saturated (h=0) during infiltration. In addition,
it was assumed that the applied NH^NOs fertilizer was dissolved
and entered the soil in 4 hours. The total amounts of nitrogen
applied in this manner was equivalent to 83 kg N/ha. Two
additional irrigations of 3.2 and 3.3 cm of water were applied
on the 48th and 62nd day of the growing season. Water losses
due to evaporation at the soil surface were included in the
evapotranspiration. A crop transpiration demand of 0.3 cm/day
was assumed throughout the simulation period. The root uptake
of water was described using the Molz-Remson model (equation
24) , while plant uptake of NIU and NO3 was simulated using the
Michaelis-Menton type model (equations 38 and 39) . The cumula-
tive amount of nitrogen absorbed by the plant was calculated by
equation (40), where the root density distributions, R(z,t) were
estimated by the empirical model described in Section 5.
The soil-water content distributions at selected times
following the three irrigations are shown in Figure 17. The
water content profile at the cessation of infiltration, t=0.5
day, of the first irrigation (Figure 17) was similar to that
shown in Figure 10. However, for larger times, the soil water
contents in the former case are lower than those for the latter
as a result of water uptake by the plant roots. A total of 4.2
cm of soil water would be transpired by the plants during a two-
week period if no water stress occurred. The second and third
irrigations of 3.2 and 3.3 cm, respectively, were smaller than
this amount, and resulted in multiple wetting fronts (Figure
17) . However, more or less uniform soil-water contents existed
in the surface at all times.
Solution concentrations of N03-N and NHit-N in the soil
profile at selected times following each irrigation are shown
in Figures 18 and 19. The position of the N03-N front
immediately at the end of the first irrigation (curve labeled
0.5 days in Figure 18) is at the 25 cm depth and can be cal-
culated by equation (49) given I = 9.1 cm and a soil water con-
tent (9f) of 0.36 cm3 /cm3 behind the wetting front. The NHit-N
front was calculated to be at the 17 cm depth; this retardation
is due to ion-exchange. During the two-day period following
the first irrigation, redistribution of soil water had caused
the N03 and NHi> pulses (Figures 18 and 19) to move to a depth
54
-------
Soil Water Content, cmlcrri
o
0.2
0.4 0
0.2 0.4 0
0.2
0.4
u
E
U
-C 20
m^mnJ
a.
_ 40
6
to
60
i u
"1st IRRG
_
••*
-
1|
1
1 /
/1
X
/
I
/
0.5 days
^2 days
'Todays
i ii
"2nd IRRG
-
i
1
I
^
/0.5days
J
( i
^2 days
J
p-*-14 days
j
i
3rd IRRri
*«^ 1 U 1 1 \ fA^T
1
I
i
|
j
1
j
21 days^i
i
I
i
i
i
^0.5 days
J
^x*^7
'}*-2. days
/
r
l •
i /«-14days
/
i
Figure 17. Simulated soil-water content distributions in, a
deep uniform loam soil profile during infiltration
and redistribution following three irrigation events,
0
NCL-N Solution Concentration , jugN/cm
0 20 4Q 6O 80 100 O 20 40 6O 80 100 O 2O 40 6O
£20
u
2 days
1s irrigation
days
,14 days
2nd irrigation
21 days
3hd irrigation
Figure 18. Simulated N03-N solution concentrations in the soil
profile at selected times following three irrigation
events (Figure 17).
55
-------
E
u
0
NH4-N Solution Cone. , ;ugN/cm3
0 20 40 60 80 100 0 20 40 60 O 20 40
, 20
O.
UJ
Q
O
CO
40-
60L
14 days N2days
1st irrigation
.14 days
2 days
2nd irrigation
Q >14.21 days
2 days
3rd irrigation
Figure 19. Simulated NH^-N solution concentrations in the soil
profile at selected times following three irrigation
events (Figure 17).
of 29 and 19 cm. The total amount of NH^-N in the soil solution
had decreased during the 14-day period (Figure 19) principally
due to nitrification and plant uptake.
Water redistribution and extraction by plant roots resulted
in a fairly uniform soil-water content above the wetting front
in the soil profile at all times during water redistribution.
Such a uniform water content with soil depth is primarily due
to the root density distribution [R (z,t)] used in this study
(Figure 5) as well as the absence of direct evaporation from
the soil surface. Selim et al.95 found that the presence of
soil surface evaporative conditions at the soil surface and
a root extraction pattern which sharply decreased with depth
resulted in a nonuniform soil-water content distribution pattern
(Figure 20). Unlike the root distribution pattern of Figure 5,
Selim et al.95 used a root distribution in which 40, 30, 20, and
10% of the total water extraction was supplied, respectively,
from each quarter (15 cm) of the root zone (60 cm depth). Figure
20 clearly shows that water uptake by plant roots resulted in a
continued decrease in the water content in the root zone (60 cm
depth). During this period, the wetting front associated with
the applied irrigation water (4 cm) advanced with time to depths
beyond the root zone.
56
-------
From Figures 18 and 19, it is clear that the first irriga-
tion of 9.1.cm caused significant movement of NHi* and NO3 in
comparison to the second and the third irrigations of 3.2 cm and
3.3 cm, respectively. The total amounts of NHU and N03 present
in the root zone continued to decrease as a result of trans-
formations and plant uptake. NH4 concentrations in soil solu-
tion (Figure 19) had diminished to less than 4 yg N/ml and that
of NO3 were less than 10 yg N/ml (Figure 18) by the 83rd day of
the growing season (i.e., 21 days after third irrigation).
SOIL WATER CONTENT , cm/cm3
0 0.05 0.10 0.15 0.20
Figure 20.
Soil-water content (9) distributions with time
during plant-water uptake and evaporation in a
uniform soil profile of Lakeland soil (from
Selim et al. ).
57
-------
The total amounts of NOs, NtU (sum of solution and exchange-
able phases), and organic-N remaining in the root zone, as a
percentage of that at the initiation of the simulations on the
34th day, are presented in Figure 21. The losses of nitrogen
shown here are due only to transformations and plant uptake as
there was no movement of soil water beyond the root zone. The
rapid transformation of NH4 is evident in Figure 21. The pro-
duction of NO3 due to nitrification was greater than that ab-
sorbed by the roots during the first week, giving rise to the
plateau in the early portion of the NO3 curve in Figure 21. The
amount of NO3 decreased rapidly after this time as N03 became
the major source of N for plant uptake. The amount of N
mineralized exceeded that immobilized during the 7-week simula-
tion period.
The cumulative amount of nitrogen removed by the crop
during 34-83 day growing period is shown in Figure 22. The
curve marked "demand" represents the amount of N required by the
-------
I
plants if maximum N-demand (Q{Jax) was satisfied at all times (i.e.,
ideal growth) . The amount of nitrogen present in the crop root
zone was insufficient during the latter part of the simulation
period (times greater than 8 days in Figure 22) to meet the
maximum demand. This resulted in a significant deviation of the
simulated curve from the "ideal" curve. Such a nitrogen deficit,
when it occurs under real conditions, would lead to decreased dry
matter accumulation and reduced yields.
^2000
^1600
*^
£
a
"0.1200
800
CD
D 400
O
34-63 day period
Demand
(idea!
Simulation
(research model)
Figure 22.
08 16 24 32 40 48 56
TIME,Days After
Application
Comparison between simulated cumulative nitrogen
uptake and that when maximum uptake demand is
satisfied at all times during the growing season.
59
-------
SUMMARY
The research model simulations presented here provide a de-
tailed description of the fate of the various nitrogen species
in the crop root zone during the growing season. However,
limitations on available input parameters and the lack of a
reliable data base do not permit verification of the research
model. Experiments involving water and nitrogen movement and
microbiological nitrogen transformations are needed for model
verification. The soils on which these experiments are conducted
must be well characterized in terms of soil-water properties.
The nitrogen concentration and water content distributions in
the soil profile should be documented at various times during
the growing season. Consideration should also be given to the
transient dynamic nature of the total system rather than initial
and final plant and soil profile conditions.
60
-------
SECTION 8
MANAGEMENT MODEL-SIMULATIONS
MODEL VERIFICATION
NaNagara et al.59 have performed field experiments to
measure nitrogen uptake by corn during an entire crop growing
season. In addition to measuring nitrogen accumulation in the
plant, these authors also obtained data on root length and
nitrate concentration distributions as well as water losses by
evapotranspiration throughout the season. These experimental
data will be utilized to verify the management model described
earlier. NaNagara et al.59 have compared their data with pre-
dictions from two conceptual mechanistic models of nitrogen
uptake by plants (Phillips et al.1*9). Model I considers the
mass flow of nitrate into roots with water (i.e., passive up-
take) as a result of water uptake by roots in response to the
transpiration demand. By knowing the amount of water transpired
in a given time period and the average nitrate-N concentration
in the soil solution in a given region of the soil profile, the
cumulative N-uptake was estimated. Model II considers the
microscopic processes of nitrate transport to root surfaces by
diffusion and mass flow. Furthermore, the rate of N-uptake by
roots was assumed to be directly proportional to the nitrate
concentration. Note that neither model I and model II considers
uptake of the NHi* species.
Additional input parameters used to simulate the data of
NaNagara et al.59 were provided by Phillips89 and were: SFC =
0.4, 9i5=0.15, R=2.0, ki=0.1 day"1, k3=k.t=0. 0003 day-1, T° =
840, TN'o.=2290, and T£rq_N=3000. The values of the transforma-
tion rati coefficients were not measured, but were selected to
represent those of Maury soil (Kentucky) on which the field
experiments were performed. A total of 18.7 cm of water was
received as rainfall during the 112-day growth season, whereas
accumulated water loss due to evapotranspiration was 23.79 cm.
The total amounts of NHi»- (solution + adsorbed) , N03 and
organic-N remaining in the root zone, as a fraction of that
present initially, during the growing season are shown in
Figure 23. These curves were plotted from the simulations
obtained with the management model. It is apparent from
Figure 23 that, although very little net mineralization of
61
-------
organic-N (74 yg) occurred, most of NH^ was rapidly transformed
during the first 40 days of the season. The total amount of
NO3 within the root zone increased up to 20 days in spite of
plant uptake, suggesting that the rate of nitrification exceeded
that of plant uptake. Beyond 20 days, however, the amount of
NOa-N decreased rapidly as NO3 was the major source for plant
uptake. As there was no loss of any nitrogen beyond the root
zone, the changes in total amounts described above were due
only to transformations and uptake.
The calculated cumulative amounts of nitrogen removed by
corn using the management model (Model III) are compared in
Table 2 with those experimentally measured by NaNagara et al.59.
Nitrogen uptake values were also predicted by the two microscopic
conceptual models of Phillips et al.1*9 (Models I and II) and
presented in Table 2. Reasonable agreement between measured
data and all three predictive models (with widely different
0
Management Model
0 40 80
TIME,DAYS AFTER PLANTING
120
Figure 23. Fraction of applied nitrogen remaining in the plant
root zone of Maury soil, simulated by the management
model, during the corn growing season.
62
-------
TABLE 2.
COMPARISON BETWEEN MEASURED NITROGEN UPTAKE BY CORN
(Zea mays L.) GROWN UNDER FIELD CONDITIONS AND THAT
PREDICTED BY THREE SIMULATION MODELS.
Growth
Period
(days)
34-49
49-76
76-97
Total
34-97
% Error
Measured
N-uptake
mg N/plant
1435
1593
974
4002
Calculated
Model I
1097
1101
1496
3693
-7.7
N-uptake
Model II
1254
2000
1278
4533
+13.3
(mg N/plant)
Model III
1928
1948
683
4559
+13.9 .
conceptualization of uptake processes) makes acceptance or -re-
jection of any of these models difficult. Close agreement be-
tween simple model predictions and measured data is encouraging
considering all the approximations and simplifying assumptions
involved in development of the management model; however,
additional testing of the management model is needed. Finally,
the input data requirements for this model are minimal in com-
parison to other models. Thus, the conceptual management model
seems to hold promise.
MODEL SIMULATIONS
The management model was used to simulate selected irriga-
tion application schemes in order to examine their relative
efficiency in maximizing plant uptake of nitrogen and thereby
minimizing nitrogen loss beyond the root zone. The soil
parameters chosen represent a deep, well-drained, homogeneous
sandy soil profile, while the crop parameters are for corn
(similar to those used earlier in Section 7). The soil hydraulic
conductivity function and the values of 9pc and 615 were those
used in Section 5 for the sand (see Equation 28).
The two water management schemes
natural rainfall with no supplemental
trolled amounts of irrigation under no
amount of irrigation water applied was
greater than the amount of soil water
gation was allowed only when the plant
within the root zone was less than 60%
able water (TAW). -Thus, the corn crop
simulated were: (i)
irrigation, and (ii) con-
rainfall conditions. The
equal to or 1.5 times
used by the plant. Irri-
available water (AW)
of the total plant avail-
simulated here was never
63
-------
under "water stress" (as defined by Eq. 27) during the simulated
120-day crop growing season. The rainfall data used as input
were obtained from weather records (for May-August, 1974)
maintained at the Agronomy Research Farm of the University of
Florida at Gainesville.' A single application of NH^NOs fertilizer
at the rate of 300 kg N/ha at planting (time=0) was assumed.
The initial amount of "mineralizable" organic-N in the 100 cm
profile was set equal to 2863 yg N/cm3. The first-order trans-
formation rate coefficients for nitrification, mineralization,
and immobilization were 0.12, 0.0024, and 0.0024 day"1, respec-
tively. The retardation factor (R) for NHU adsorption was set
at 1.57. The entire soil profile was assumed to be initially
at "field capacity" soil-water content (eFC=0-08 cm3/cm3).
The position of the nitrate pulse in the soil profile during
the growing season, simulated for three water application schemes,
is presented in Figure 24. Also shown is the progression of
maximum depth (L) in the soil profile to which plant roots had
grown. The nitrate pulse resides well within the crop root zone
during the entire season for the case in which the amount of
irrigation water was equal to that depleted by the crop (curve
labeled 1.0 ET in Figure 24). For the case in which the amount
120
E
u
Q_
UJ
Q
O
80
40
0
SIMULATED IRRIGATION SCHEMES
0
Figure 24
30 60
TIME, DAYS AFTER
_L
90
PLANTING
120
The predicted depth of nitrate front under three
water application schemes during the growing season
in a sandy soil profile. Increase in the maximum
root zone depth (L) with time is also shown.
64
-------
of irrigation water applied was 1.5 times that required by the
crop (curve labeled 1.5 ET in Figure 24), the nitrate pulse was
leached beyond the root zone after about 65 days. The intensity
and the frequency of the rainfall events chosen here was such
that the nitrate pulse was leached rapidly out of the root zone
very early in the season (only five days after planting) as
indicated by the curve labeled "rainfall" in Figure 24. Such
observations are not uncommon in field studies involving sandy
soils in Florida. A few major rainfall events of approximately
5 cm each can essentially move the fertilizer nitrogen out of
plant root zone.
The effect of simulated water application management
schemes on the cumulative nitrogen uptake by corn is illustrated
in Figure 25. The "ideal" uptake demand for nitrogen was met
under the 1.0 ET treatments at all times. This was possible
since the nitrate pulse resided within the root zone and was
available to roots for absorption in sufficient quantities.
The "ideal" demand, however, was not satisfied for the 1.5 ET
treatment; the time at which this curve deviated from the "ideal"
(Figure 25) corresponds to the time when the nitrate pulse was
leached out of the root zone (Figure 24). The cumulative
nitrogen uptake curve for the rainfall treatment deviates
significantly from the "ideal" curve at all times as could be
surmized from Figure 24.
65
-------
CM
U
CT
E
LU
2.4
CL
LU
CD
O
ce
h-
>
h-
<
_J
Z>
z>
U
1.6
0
1.0 El'
Management Model
IDEAL
DEMAND
0 40 80 120
TIME, DAYS AFTER PLANTING
Figure 25. Cumulative nitrogen uptake by corn grown in a sandy
soil under three water application schemes, as
simulated by the management model.
66
-------
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75
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76
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APPENDIX A
DESCRIPTION OF THE COMPUTER PROGRAM
FOR THE RESEARCH MODEL
The Northeast Regional Data Center (NERDC) of the State
University System (SUS) of Florida at Gainesville, FL is
equipped with an AMDAHL 470 V/6-II computer. The Amdahl com-
puter is software-compatible with IBM 370/165 computers. The
numerical solutions comprising the research model (Section 4)
required a total of 256K bytes of main storage for execution.
Actual CPU (computer processing units) time required for a given
simulation run will increase with increasing intensity and/or
frequency of the water input events. As an example, CPU time
for the three irrigation events discussed in Section 7 (page 50 )
was 25, 5, and 5 minutes, respectively. Recall that the first
event included the infiltration of 9.1 cm of water over a 12-hour
period, while 3.2 cm of water infiltrated in 4-hours in the latter
two events.
The computer program consists of a source program and
seventeen subprograms, and an input data section. The names of
the subprograms are AXISPL, GRAPH, CHECKT, WATER, MOISD, INITWT,
SBCW, INITST, DADJ, DADJD, CHECKN, AMONIA, NITRAT, GASORB, OUTPUT,
TINT, and TRIDM. In addition, there are five subroutine func-
tions namely; ZZ1, ZZ2, ZZ3, ZZ4, and ZZ5. The user of this
program must provide parameters in the form of punched data cards
in the data section, and as FORTRAN statements in the SBCW and
WATER subprograms as well as subroutine functions ZZl, ZZ2, ZZ3,
ZZ4, and ZZ5. The remaining source program and subprograms need
not be altered and remain valid for all situations.
The main function of the main program is prescribing the
DIMENSION and COMMON statements, reading input parameters, and
establishing the entire sequence of the program. Subprograms
INITWT, INITST, and MOISD provide the initial distributions of
all the variables and calculates Az and At according to the
stability criteria. Subprogram SBCW provides h at z=0 according
to the boundary condition for the water flow equation, which may
be altered by the user as desired. Subprograms WATER, AMONIA,
and NITRAT provide the solution for water head (h) , NHi^ concen-
tration (A) and N03 concentration (B), respectively. Subprogram
GASORG calculates the amount of organic-N and gaseous-N. Sub-
program TRIDM provides the solution for a linear system of
equations with a tridiagonal coefficient matrix. Subroutine
77
-------
functions ZZ1, ZZ2, ZZ3, ZZ4, ZZ5 are used in conjunction with
subprograms AMONIA , NITRAT, and GASORG and provide the reaction
rate coefficients, (ki, k2, k3, k4, and k5) as a function of
soil water suction, soil-water content and/or organic-N content
at every time step and incremental soil depth.
The dispersion coefficient D and the hydraulic conductivity
K are calculated at each time step in the WATER subprogram. Here,
D and K are provided as a function of (q/9) and 6, respectively.
In addition, Cap(h) and conversion of h to 6 at all incremental
points in the soil profile were calculated in the WATER subpro-
gram. This conversion is based on the 9 versus h relationship
(in a tabular form) for each soil.
An important feature of the program is that increments of
Az and At are adjusted automatically to satisfy stability and
convergence criteria for the water and solute finite difference
equations. These adjustments are carried out after every 20
time steps using subprograms DADJ and DADJD. Another program
feature is that the number of nodal points (increments) are
automatically calculated from the length of the flow region (soil
profile). Only that portion of the flow region where water and
solute are present is considered. The adjustments of the number
of nodal points are made using subprogram CHECKN. This number
is checked every 20 time steps, and no further changes of the
number of increments will occur when the total column length is
reached. This feature minimizes the unnecessary use of a large
number of nodal points and saves considerable CPU time. A third
feature of the program is that output data and plots are pro-
vided at specified times. This adjustment is carried out using
subprogram GHECKT, where t's are continuously adjusted until the
prescribed times are reached. For each prescribed time; h, 6,
K, q, NtU-N, NOs-N, organic-N, gaseous-N throughout the soil
column are printed using subprogram OUTPUT. Subprograms AXISPL
and GRAPH plots (using GOULD plotter) for 6, NHi», NO3, and
Org-N versus depth for various times can also be obtained. The
scale and length of each plot is prescribed in these subprograms
and may be changed by the user.
PROGRAM PARAMETERS
The following parameters are inputs to be provided in the
DATA section of the computer program
NX = number of data points of the soil water characteristic
relationship (0 versus h),
THC = water content 6 from soil water characteristic rela-
tionship (dimension = NX), cm3/cm3,
HC = corresponding water suction h from soil water
78
-------
characteristic relationship (dimension = NX), cm,
DZ = initial approximation for Az, cm,
DT = initial approximation for At, days,
DISP = initial approximations for dispersion coefficient D,
cm2/day,
THMIN = estimated minimum soil water content, cm3/cm3,
THMAX = maximum soil water content, cm3/cm3,
NT = number of prescribed times at which data are desired,
TIT = times at which output are desired (dimension = NT),
days,
NTGR = number of prescribed times at which plots (using
GOULD plotter) are desired,
TGRAPH = times at which plots are desired (dimension = NTGR),
days,
RKD = K (see equation 13), cm3/g,
RKl = ki (see equation 6a, 6b), day"1,
RK2 = k~2 (see equation 7), day"1,
RK3 = k~3 (see equation 8a, 8b) , day"1,
RK4 = k\ (see equation 9), day"1,
RK5 = k~5 (see equations lOa, lOb) , day"1
ZZ1 = ki (see equations 6a, 6b), day"
ZZ2 = k2 (see equation 7), day"1,
ZZ3 = k3 (see equations 8a, 8b), day"1,
ZZ4 = kn (see equation 9), day"1,
ZZ5 = ks (see equation lOa, lOb), day"1,
NTT = number of points for initial distributions of water
and nitrogen species in the soil profile,
XXX = depths at which initial distributions are given
(dimension = NTT), cm,
79
-------
Cl = initial distribution of water suction (h) in the soil
profile (dimension = NTT), cm,
C2 = initial distribution of soil water content (6) in the
soil profile (dimension = NTT), cm3/cm3,
C3 = initial distribution of NHt, in soil solution
(dimension = NTT), yg N/cm3,
C4 = initial distribution of N03 in soil solution
(dimension = NTT), yg N/cm3,
C5 = initial distribution of organic-N per gram soil
(dimension = NTT), yg N/g soil,
C6 = initial distribution of gaseous-N per gram soil
(dimension = NTT), yg N/g soil,
ROU = p, soil bulk density, g/cm3,
COLUMN = length of soil profile, cm,
TSALT = length of time of solute application, days,
TWO = length of time of water infiltration, days,
CONST = hydraulic conductivity at saturation, cm/day,
AC = a coefficient for K versus relationship,
BC = a coefficient for K versus relationship,
CSNH4 = concentration of NHn. in applied solution, yg N/cm3,
CSN03 = concentration of NOa in applied solution, yg N/cm3,
DFLUX = evaporative flux during water redistribution (time>
TWO), cm/day,
Input parameters to be provided in subprogram WATER are
CON = water hydraulic conductivity K, cm/day,
DISPC = dispersion coefficient D, cm2/day,
Input parameters to be provided in subprogram SBCW is
H(l) = water head h at z=0 during infiltration and maximum
h during redistribution, cm,
Other notations used in the program are:
80
-------
TH = soil water content, cm3/cm3,
H = water suction, h, cm,
CNH4 = concentration of NHij in soil solution, A, yg 11/cm ,
CN03 = concenttatiua of N03 in soil solution, B, yg N/cm ,
CORGN = amount of orxjanic-N per gram £,oil, CM, yg N/'g,
CN02 = amount of gaseous-N per.gram soil, G, yg N/g,
CAP = soil water capacity, Cap(h),
WFLUX = soil waler flux, q, cm/day.
81
-------
APPENDIX B
FLOW CHART OF THE COMPUTER PROGRAM
r~*\ ii -1,100 /
82
-------
APPENDIX C
FORTRAN PROGRAM LISTING
CCMMCN/LI/
*VPI PIC I «DISPC( fit
COMMCN/L2/ «Mein).EE(eiO>.CC(6IC).R(61C).XC61")
COMMON/L3/ N,NM1,NM2,NP1,NP2
CCMMCN/L4/ ALPHA, BETA. CT.DZ
COMMON/L5/ PK.C.RK1,RK2,RK3,RK4,RK5
COMMCN/L6X SFLUX,CSNt-4,CSNO3
COMMON/L7/RCg, COLUMN .DFLUX
COMMCN/L8/ DISP.THMAX.THMIN.HMIN.CORGNI
COMWCN/LS/tlfrE.TPRINT.TWRITF
COMMON/LI O/ H , CAP< 81 0 )
CC«tMCN/Lll/ THCt40).l-C«4e),CAPC(4'5 >
COMMCN/tl2/ AC. BCiNXtNXl .CONST
COMMCN/U13/ MFLUX(SIR)
CQMMON/U14/ VO.TWO.TSALT
COMMON/LI 5X TIT<3^) .TC.DTDT.IT, IL.NT
CCMMCK/L16/IC, IWT
COMMCN/L17X X XX<3<>) ,C1 ( 30 ) ,C2( 33 ) ,C 3( 3" » ,C4 < 3C> ,C5 1 30 ) . C6{ 3C)
COMMON/H9/ TGRAPM15).NTGR,ITGR
100 FORMATC8F10.3)
23C FORMATI5E1 C-.4)
300 FORMAT <2 14)
REAOI5.3Cri NX
NX1=NX-1
READ(5.10T> ITHC( I ).!=!. NX)
WRITEC6.1CT » t THC( I ) .1=1 .NX)
(t-C(I > .1 = 1 .NX)
PEADC5.1PO> 02, OT
WRITEI6.10C ) CZ.DT
RSAD ( 5. ICC) CISP. TH*AX . THM IN . HM I N , COP GN I
WRITEC6.100) DIS°, THMAX.,THMIN.HMIN.CORGNI
RE AD ( 5 . 1 C C ) COLUMN, ROU. CSNH4 ,CSNO 3 . DFLUX
CCLUMN.POli.CSNH4.CSNO3»OFLUX
AC.BC.CCNST
*R1TE(6,2«0) AC.BC.CCNST
REAOiS.SOO) NT
REAOCS.l^O ) iTITCI ),! = !, NT)
»PITE(6.1CC) (TIT( I ),! = ! .NT)
R NTT
(XXX(T ) ,1 = 1, NTT)
CXXXf I ) .1=1. NTT)
.1 = 1, NTT)
1.1 = 1. NTT)
,1=1. NTT)
).!-». NTT)
,1=1 .NTT)
). 1 = 1. NTT)
.1 = 1. NTT)
),!=!, NTT)
,1=1. NTT)
>.!=!. NTT)
,I=t.NTT)
1.1=1. NTT)
NTGR
REAO(S.IOO) CTGRAPKI ) .I = 1.MTGR)
VI^ITEie.tOC) (TGRAPHd ) ,1 = 1 .NTGR)
F»PAD<5,1C"5) FKD.RK1 , RK2 ,PK3 ,RK4 ,RKf
»RITE«6.10T ) RKO,BK1.KK2,RK3.RK4,RK5
ITGR=1
CO 2 1=1, NTT
CK I >=-4q'?c.o
C2ii)=c.ir<:
IT=1
TC=TIT< IT)
NM1=N-1
NM2=N-2
NP1=N+1
NP2=N+2
TSALT=1 .CO
READC5.1r'3 ) (CHI
»RITEI6.inO) ) (C4(I
*RITE(6.nO) CC4{
REAOiB.lO^)
-------
CALL IMTUT
CALL INITST
IC=2
IWT=-1
CALL AXISPL
)=-JT.O
THMIN=C.1?
COLUMN=90.0
COLUMN=45.C
CALL SECW
IL=250
IL=20
IL=*?
IL=1 0«
99 CONTINUE
00 5 I 1=1 , IL
CALL WATER
CALL AkCNIA
CALL NITRAT
CALL GASORG
5 CONTINUE
TIME=TIME+IL*DT
WRI TE( 6.2CO) CZ.OT, TIME. ALPHA, BET A
CALL DADJ
WRITF<6,20C> DZ.DT .TIME. ALPHA, BETA
TWRITE=ABS(T 1ME-TCR#PH( ITGOJ )
IFIT1KRITE.LE .1 .OF-3 ) CALL GRAPH
IF( TIME.GE .T ITCNT) ) CALL PLOT <0 .0 ,« .0 ,999 >
TV*RITE=ABS(TIME-TC )
IF
-------
SUBROUTINE HATER
COMMCN/L1/ THteiP)•CNH4(810),CNO3<610).CORGN<810),CNO2t810),
*VP( 810),DI£PC(610)
COMMCN/L2/ *A(eio>.EE(61fl
COMMCN/L3/ **Mil »N»2,NF1 , NP2
CCNMON/L4/ ALPtlA.BETA.CT.DZ
CQMMCN/L5X RKD.RK1. RK2.RK3.RK4,RK5
CQMMCN/L6/ SFLCX,CSNH4.CSN03
COMWCN/L7/ POU
CCMMCN/L8/ CISP.THMAX.THMIN.MMIN.CORGNI
COMNON/L9/1IME.TPRINT,T»|RITE
COMMCN/HO/ HI 810),CON(810),CAP( 810)
COMMCN/L11/ THC(40).HC(40),CAPC(40)
COMMCN/L12/ AC.BC.NX.NX1.CONST
CCMMCN/L13/ MFLUX(aiO)
COMMCNXL14/ VOtTWD.TSALT
CU1=40.C
AO=AC/JOO.O
NCL 1=CL1/DZ+C.C(310
NCL2=NCL1+1
NCL3=NCL1*2
DO 90 I=1,NP1
90 CON«I)=AC*EXP«eC*(TK U4TH( 1*1 ) )*C.50>
IF( NCL3.GE.NF1 ) GO TO 92
DO 91 I=NCU3,NP1
91 CONd ) = AO*EXP( BC*(TK I )+TH( I *1 J )*0 .51 >
CON (NCL2) = (CCN(NCL1 )*CCN(NCL3) ) *2/ ( CON *CON ( IJ )
6B(I)=-ALPHA*CCN(I*l)
CC(I)=-ALPHA*CCN(1*1)
1 CONTINUE
AAtNMl)=CAP(K)*ALPHA*CCN(N)
DO 2 1=1.NM1
XI=CAPC 1*1 )*K 1*1 )
X2=AI_PHA*CCN(I »*H( I )-ALPHA*H( !*!)*( CO N( 1*1 I *CON ( I ) )
X3=ALPHA*CON(I*l)*H(I*2»
X4=-BETA*(CCM 1*1 )-CCN< I) )
R(I ) = X1*X2*X3*X4
2 CONTINUE
R(l ) = R(1 >**LFHA*CCM1 >*H( 1 )
CALL TRIOM(AA,ee.CC.R.X,NMl)
DO 3 K=2,N
3 H(K)=X(K-1)
H(NPl)=h(NJ
H(NP2)=H(N)
CALL SBC*
DO 15 J=1.NP2
IF(H(J»,LT.hC(1)J GC TC 25
TH(J)=THC(1)
15 CAP(J)=CAPC(1)
25 CONTINUE
OO 60 I=j.NP2
DO SO K=ltKXl
IF(H(I).GT.*C(K*1») GC TO 70
80 CONTINUE
70 TH(I >=THC( K)*CAPC(K)*«K I >-HC(K)»
IF ) TH(I)=THC(1)
CAP(I)=CAPC(K)
6^ CONTINUE
OH 95 1=1.KP1
WFLUXd )=-CCN< I)* (HI 1*1 )-H( I »/DZ*CON( I J
DISPC( I >=r> .02560*^. 1274?*ABS(WFLUX( I »/TH(I ) J**1.3550
9= CONTINUE
RFTURN
END
85
-------
SUBRCUTIKS >fQNIA
C NH-4 PRGRAI*
CCHMCN/L1/ THCSIO) ,CKH4(81Q I . CN03< 8 1 0 ) . CORGN< 8 10 ) ,CN02< 8 1 0 I .
*VP< at OJ.DJ SFC(eio)
CCMMCN/L2/ /MC 1") , Ee(61C).CCC610> ,R<610) ,X<610)
COMMON/L3/ N.M<1,M»2.MF1.NP2
CQMMON/L4/ ALPHA .BETA. DT.DZ
COMMON/L5/ RKD.RK1 ,RK2 .RK3.RK4.RK5
COMNON/LS/ SFLLX.CSNH4.CSN03
CCMMCN/L7/ POU
COMMCN/L8/ CISF.THMAX.TMKIN.HMIN.CORG.NI
COMMON/L9/T I ME . TPR I hT . TWR I TE
COMMON/L10/ Ken ) ,CCN( 810 ),CAP(8JO )
COMMCN/L 11 / THCC4T) .HC < 40 ) ,C ARC (40 I
COMMON/L12/ *C.BC, NX, NX1, CONST
COMMCN/L13/ *FLUX(810>
COMMON/L14/ VO.TWD.TSALT
COMMON/U15/ TITO") .TC.OTOT, IT.1U.NT
FF=2.0*OZ
SSINF=I«FLU)I<1 )
CNH4C1 » = CSSI^F*FF*CSIMM4+DISP*TH^1)*CNM4(3) »/C SSINFK-FF+OI SP*THC
DO 1 1=1. NP1
OISP=DISPC< I)
VP( I >=»FLUX( I >-DI SP*(TH< I»l )-TH( I ) )/DZ
1 CONTINUE
IFfSFLUX.LE.O.OI GC TO 13
C
C
DO S I'1'.M«2
OISP=DI SPC( I-H )
RKK=1.C+RKO*POU/TH« 1*1 )
AA< I )=RKK+2.C*ALPH *C I SP-6ET A* VP( 14-1 )/TH( 1*1 )
AA( I )=RKK+2.0*ALPHA*OISP
8B( I )=BETA*VF« 1+1 »/TH( 1+1 )-AL^HA*DI SP
88( I )=-ALFHA*OISP
DISP=DISPC< 1*2)
CC< I)=-ALPH>*DISP
5 CONTINUE
OISP=DISPCCN)
RKK=1 .0*RKD*FOU/TH(S)
AA(NM1 )=RKK4ALFHA*DISP
DO 10 W^l.MDl
I=M+1
DISP=DISPCJ I )
RKK=1 ,0*RKO*POC/TH ( I )
R(M)=RKK*CNH4C I ) +ALFHA*DI SP* /TH( I))*(CNH4< I*1)-CNH4( I) )
1C CONTINUE
DISP=DISPC<2)
Rll )=R ll)*ALFHA*DISP*CNH4l 1 )
GO TO 14
C
13 CONTINUE
CMH4C1 )=CNH4C2)
DO 11 1=1. KM2
DISP=DISPC
AA{ I ) =R KK + 2.0*«_PHA*D ISP-BET A* VP< 1 + 1 )/TH(I*l )
BBC I)=BETA*VP(I*l »/TH( 1+1 > -ALPHA*DI SP
DISP=DISFC( 1*2 )
CC( I ) = -ALFHA*DISP
1 1 CONTINUE
OISP = DISPC(N >
RKK=1 ,"*RKD*FOU/TH(N>
AA< NM1 I=RKK*ALPHA*DISP
DISP=OISPC<2 )
RKK=1 ,0*RKD*ROL/TH(2I
AA( 1)=RKK*1 .'<*ALPHA*DISP-B€TA*VP( 2)/TM( 2»
OO 12
I=M*1
DISP=DISPC( I )
RKK=1
9{M)=RKK*CNH4( I ) + ALPHA*CI SP* (CNH4 < 1*1 )-2.0*CNH4( I)*CNH4( I- 1 ) )
ZK1=ZZ1(RK1.TH( I ),H{I ).Z,TIME)
ZK3=ZZ3«RK3.TH(I ) . H( I ) , Z.T IME)
RCM) = RIM)-DT*< ZK1*RK4)*CNH4{ I ) * (ROU*DT/TH( I ) )*ZK3*CORGN< I )
12 CONTINUE
14 CONTINUE
CALL TRIOM(AA.B8.CC.P.X,NM1 >
CO 15 I=Z.N
15 CNH4( I ) = X< 1-1 )
CNH4
-------
SU«3 ROC TINS MTRAT
NO-3 PRGRAW
CQMMCN/L1X TH(ei^) . CNH4 < fl 1 1 J .CN03C3 1 « 1 .CORGNf 81 1 ) t CNC2< 3 1" ) .
*VP< ai"> ,DI SPC< ei"1)
COMMCN/L2/ *A),R<61'<),
CQMMQN/L3X N«NM tM>2.NPl«NP?
CQMMON/L4X ALPHA .BE T A . CT.OZ
CQMMONXL5X FKD.RK1 . PK2 .PK3.RK4 , PK5
COMMCNXLfiX SFLLX.CSNH4 .CSNO3
COMMCN/L^/ BOU
COMMCN/LS/ DISF .THW AX t TH* IK, HM I N, CORGNI
COMMON/L9/T I KE .TPR I NT , TWR I TE
CQMMON/HAX K6inj . CCNC 81 0 ) . CAP ( 8 1
COMMCN/LU/ THC<4ri) .HC ( 40 ) ,C ARC (4« )
COMMCNXL12/ AC , BC. N >. NX 1 , CONST
CC««MCN/tl3/ WFLUX(81^)
COMMON/L14/ \0,T»0,TSALT
SSINF=mFLUX( 1 )
CNQ3U > = *CNO3(3> )/( SSINF*Ff=+DI SP*TH<
IF(SFLUX.l_E.O.O J GC TC 13
00 5 1=1. KM2
DISP=DISPCI I«l }
AA( I ) = | . "4-2 . f*ALPHA*C ISP-BET A* VP( I + l )/TH(I + l )
BBt I ) = BETA*VP{ 1*1 J/TH( 1 + 1 J -ALPHA*D ISP
OISP=DISPC< I+2>
CC( I )=-ACPHA*OISP
CONTINUE
OISP=DISPC(N)
AA( NH1 »=1 .C4ALPHA*CISP
DO 10 M=1.NM1
DISP=OISPC< I )
R
33 ( I ) = BETA*VPC I + 1)/TH( 1*1 )-ALPHA*D ISP
OISP=DISFC( I+2)
CC( I )=-ALPHA*DISP
11 CONTINUE
DISP=DISPC(K )
AA( NX1 >=1 .C+ALPHA*DISP
DISP=DISPCC 21
AA(l)=l.r + l.'?*ALPHA*CI SP-EETA*VP(2)/THf ? )
00 12 M=1.NM1
I=M+1
OISP=OISPC< I )
R(MI=CN03< I>* ALPHA*riSP*«CNO J( 1+1 )-2.?*CNO3< I J+CN03( t-1) I
Z=CORGN(I )/CCRGN(l )
ZK1=ZZKRK1.TH(I),H(I),Z,TIME)
ZK5iZZ5(RKf ,TH< I > . H ( I ) . Z , T IME)
R(M)=R=X< 1-1 >
CN03(NP1 )=CNC3 (N)
R=TUPN
END
87
-------
FUNCTICK ZZHRK1 tWC.hH.Zt TIME)
zzi =*.o
*H=-HH
IF(WH.GT.15Cf>n .0 ) RETURN
IF( WH.GT .1" .0) GO TC 1
RETURN
1 IF(WI-.GT.5? .0) GO TO 2
R^TUPN
2 IF(WI-.GT.lCr .0 ) GO TO 3
RFTURN
3 IF( ah.GT.433 .0 ) GO TC 4
ZZ1 = RK1*( "!.5r"+< WH- 1^0.
RETURN
4 ZZI =RKl*< 1
RFTURN
'. OC 1
L=VFL 21
ZZ2
FUNCTICN ZZ2CRK2tWC»WH,Z,TIME>
ZZ2=RK2
RETURN
LEVEL 21 ZZ3
FUNCTICN ZZ3CRK3,WC.I-H,Z»TIME)
ZZ3=C.O
WH=-HH
IFC WH.GT.2CCO".'') RETURN
IF! WH.GT.50.0) GO TC 1
DATE = 77CQ7
DATE = 77097
RETURN
t IFtWH.GT.20C .0 ) GO TC
RETURN
2 CONTINUE
ZZ3=RK3
IF( Kh.GT. 2000.0) ZZ3=RK3*<1 .0-0 .C5C*«HX t OOO .0 )
RETURN
END
LEVEL 21
ZZ4
DATE = 77097
FUNCTION ZZ«(RIC4.»»C.I*H.Z,TIME>
ZZ4=RK4
RETURN
END
LEVEL 21 ZZE
FUNCTICN ZZEJRKS.WC.WH.Z.TIME)
DATE = 77097
ZZ5=0.0
IF( f*C/*SAl) .LT.^.8") PFTURN
ZZ5=RK5*fWC-0.eO*WSAT)/C".n*WSAT)
ZZ5=ZZ5*Z
88
-------
SUBROUTINE I
COMMON/LI/ THiei"> ,CNH4( 8 1 » ) ,C NO3C 8 1 0 > . CORGN<810» .CNO2O10) .
*VP«810 ),DISFC<810»
COMMON/L2/ */»(61?».Ee(610),CC(610).R(6l«|,xC610>
COMMON/L3/ N.NNl .N*£ , NF 1 , NP2
COMMCN/L4/ ALPHA. BETA. CT.DZ
COMMON/L5/ RKD.RK1 . FK2 . KK3 ,RK4 , RK5
COMMQN/L*/ SFLI.X.CSNH4 .CSNO3
COMMCN/L7/ PCU
COMMON/US/ C ISP,THMAX,THMIN.HMIN,CORGNI
COMMCN/L9/lIfE,TPRINTtTWPITE
COMMON/LIT/ mei-M .ccN ,C APC ( 4« )
COMMCN/L12X AC « BC . ^ X . NX1 • CONST
COMMCN/L13/ WFLUX(8tO>
COMMON/L14X VO.TWD.TSALT
COMMON/U17/ XXXI 3^) ,C1 (31) ,C2{30) ,C3 { 3" ) ,C4 < 3^ ) , C5 (30 ) ,C6< 3C )
DO 5 1 = 1, NX1
CAPCC I)=(TI-C{I+1 )-ThC( t ) >/(HC( I*t »-
5 CONTINtr
CAPC(NX1=C AFC(NX! )
C
C
6 CONTINUE
ALPHA=DT/C 2 .0*CZ*CZ )
3ETA=DT/DZ
TTT=TTT*ALFHA
IFITTT.LE.2.00 I GO TO 8
IFCDZ.GP.O .090) GO TC t
DZ=fZ*2.0
GO TC e
7 DT=DT/2.^
GO TO 6
8 CONTINUE
CALL MCISOCI.NF2)
CALL SBCW
DO 25 1=1. ^P^
OO 15 K=1.NX1
IF4H( I) .CT ,I-C(K + 1 ) ) GO TO 20
15 CONTINUE
?<" CAP( I )=CAPC(K)
25 CONTINUE
RETURN
89
-------
SUBROUTINE INITST
COMMCN/L1/ THieiC) , CNH4C 81 «> » ,CNC3 < 81 0 ) , COPGN< 810 ),CNO2<810) .
*yp(6io» ,oiEPC( ei?>
COMMCN/L2/ AM6l").EE<610 ).CC<610) ,R(610).X(61"I
COMMON/L3/ K ,NK1 ,NK2 .NP1.NP2
COMMCN/L4/ AL°HA,BETA,CT,DZ
COMMON/L5/ RKD.PK1 . BK2 . PK3. RK4 , RK5
COMMON/L6/ SFLCX.CSNH4.CSN03
COMMCN/L7/ PCU
COMMCN/L8/ OISP,THMAX,THI«IN,HMIN,CORGNI
CQMMCN/L9XT I ME . TPR I NT, TXRITE
COMMCN/L10/ HC610) . CON ( 8 1 <* I . CAP ( 81 0 )
COMMON/L11/ THC<*n) ,HC<4") .CAPCi*? )
COMMON/LI 2/ AC.BC.NX ,NX1 .CONST
COMMON/U14/ VO.TWD.TSALT
COMMON/LI?/ XXX (31) ,CU30),C2t 3 0 ) ,C3( 30 ) ,C4 < 30) ,C5 ( 31? ) ,CC( 3 C I
THAVR=(THI*AX4THMIN>/2
1 CONTINUE
APAR=SFLUX-DISP*(THMIN-THAVR)/DZ
A.PAR=SFLUX-CISP*(THI»IN-THMAX>/DZ
VO=APAR/TH*Vfi
V5=SFLUX/THI»AX
VO=APAR/T(-MIK
ALPHA=DT/f 2 .C*CZ*OZ )
BETA=DT/DZ
' .5C*OZ/V<*
IFCOZ.GT.DVC ) GO TC 2
IF(DT.CT.DZVO) GO TC 3
GO TO 4
2 CZ=CZ/2
GO TO 1
3 OT=DT/2
GO TO 1
4 CONTINUE
C CONTINUE
AI_PHA=DT/C2.C*CZ*OZ )
BHTA=DT/DZ
TTT=CONST/CAPC ( 1 )
TTT=TTT*ALPhA
IFt TTT.LE.2.CO) GO TO 8
GO TO 6
8 CONTINUE
CALL MCISC(1,NP2)
RFTUPN
END
90
-------
SUBROUTINE TINT
COMMON/LI X THCei<5> .CNHA(et?> »C N03 < 81 0) .CCPGN (8 1 0 ) , CN02 <8 1 " ) ,
*Vt»C810) .DISPC< 810) :
CCMMCN/L2/ AA<61.5/.
*SX. 'TOTAL M— 4 IN SCIL SOLUTION PHASE. MG *«»Flfl.S/.
*5X. 'TOTAL Nh-4 IN SCIL. MG =».FlC.5/»
3CC FORMATJ5X,' TOTAL NO-3 IN SOIL SOLUTION. MG='.Ft0.5/.
*SX, 'TOTAL ORGANIC N IN THE SOIL. MG ='.F10.5/.
*5X, 'TOTAL N RELEASED FRCM THE SOIL. MG ='.F1-).S//1
DO 5 1=1. NP1
Xtl )=TH( I)*CKH4(I)
5 CONTINUE
CALL QSFCDZ.X. AA.NP1)
TNH4C=AA(NP1 )
CALL QSFCDZ.CNH4.AA.KP1 )
TNH4SS=AA|KFl)*i:OU*RKC
TNH4T=TNH4C*TNH4SS
00 10 1=1, NPl
X(I )=THCI )*CN03(I)
10 CONTINUE
CALL QSFtDZ.X. AA.NP1)
TNO3=AA=RCU*CNC2CI»
2
-------
SUBROUTINE CAOJ
COMMON/LI/ TH<81*> .CNH4( 81" ) iCNC3( 810 ) ,CORGN< 810 J ,CN02< 8 I"? ) t
*VP(aiO).DISFC(PlO)
COMMON/L2/ *MtlO) ,E6(610 ),CC<61 «>,R<610).XJ610)
COMMCN/L3/ K ,M>1. M»2 . NF1 . NP2
COMMON/L4/ ALPHA.BETA.CT.DZ
COMMCN/L5/ F.KO.RK1.RK2.RK3.RK4,RK5
COMMQN/L6/ JFLlJX,CSNH4,CSNO3
COMMON/L7/FCU,COLUMN,DFLUX
COMMGN/L8/ CISPtTHMAX,THMIN.HMIN.CORGNI
COMMON/L9X TIME, TPRINT,T»RITE
COMMONXL10/ H(810).CONC810),CAP(610)
COMMON/L11/ THCl«0),HC(4CI,CAPCC4C)
COMMON/LIZ/' AC.BC.NX.NX1 .CONST
COMMCN/L13/ »FLUX(810)
COMMON/LI4/ VO.THD.TSALT
COMMON/LI?/ XXX(30).C1(30),C2(3T),C3(30),C4(30),C5<30),C6(3C)
IF ) GO TO 11
OZVO=0.50*D2/V1
IF((OT*KKI.LT.CZVO) DT=DT*KK
ALPHA=DT/<2.1*CZ*OZ)
BETA=OT/DZ
11 CONTINUE
IFfABSCTH(L)-THMIN).LT.r.05501 RETURN
OV3=0.5C*DISPC(L)/V1
IF<
CNH4(KI)=CN|-4(I )
CORGNiK)=CCRGN(I)
CNO2(M)=CNCJ(I)
OISPC< C) = DISPC(I)
M=M+1
15 CONTINUE
CALL MOISDCH.NF2)
00 35 I=M.NP£
DO 25 K=J.NX1
IFCH
-------
SUBROUTINE CAOJD
COMMON/LI/ TH( 810) .CNH4C810 I ,CN03<810» . CORGN( 8 1 0 ) , CNC2< 8 1 0 ) .
*VP<811) ,CISFC( 810)
CGMMON/L2/ tf ( 61 0> » EBf 6 1 0) ,CC{ 61 0) .R(610),X(6ir»
COMMON/L3/ N.M»1.NM2,NP1,NP2
COMMCN/L4/ ALPHA. BETA. CT.DZ
COMMCN/L5/ PKO.RK1 . RK2 . RK3 • RK4 . RK5
COMMCN/L6/ SFLOX.CSNH4.CSN03
COMMON/L7/ FOU
COMMON/L8/ DISP.THMAX.Tf-MIN.HMINtCORGNI
CQMMCNXL9/T I f E .TPR I h.T . TWR ITIt
COMMON/L10/ H<610) .CCNC81 0), CAP (810!
COMMON/LUX THC<4 GO TO 5
RETURN
5 CONTINUE
00 15 1 = 1 ^Pl .KK
H
-------
c
SUBROUTINE OECKT
COMMGN/L4/ tLPHA.BETA.CT.DZ
COMMON/L9/TIKE.TPRINT.TWRITE
CCMMON/L15/ TITO") .TC.CTDT, IT, IL.NT
OTDf=DT
TWRITE=ABS(TIME-TO
IF(T*RITE.LT.l.OE-3) RETUPN
TIME1 f>=TIME+IL«DT
IF«TIME.LT .TCl.AND.ITIMEl O.GE .TO ) GO TO 30
RETURN
3C OT=CTC-TIMEI/IL
ALPHA=DT/t 2.0*CZ*CZ)
BETA=OT/DZ
RETURN
END
c
SUBROUTINE 1BI CM(A.E,C,D,X,N)
DIMENSION A(l),e(l),C(l),D(l),X(l)
DO 1 1 = 2,N
C(lTl)=C-(C(I-M*E(I-l))
1 CONTINUE
X(l)=0(1)
DO 2 1=2.N
2 CONTINUE
X( N)=X( N)/A(N)
DO 3 1 = 2. N
X .CNO3( 81 0) ,CORGN( 810 ) ,CNC2< 81 0 I .
VP(61C1 ,DISPC(6IO)
COMMQN/L3X * .N* 1 ,N»«2 .KFl ,NP2
COMMCN/L4/ ALPI-A.BETA.CT.DZ
CQMMCN/L5X BKD.RK1 .RK2 ,RK3 »RK4 . RK5
COMMON/L6/ SFLUX.CSNK4.CSN03
COMMON/L7/C CU. COLUMN .OFLUX
COMMON/LS/ DISF.THMAX.THMIN.HMIN.CORGNI
COMMCN/U9XTIt»E.TPRIKT.T»(RITE
COMMCN/LtO/ H(eiO) ,CCN( 81 D >. CAPCS10 )
COMMON/LI I/ THC«40I .HC(40 ).CAPC<40)
COMMCN/L12/ AC.BC.NX.NX1 .CCNST
COMMON/LI 3 / kFLUX(BlO)
COMMON/1.14/ VO»TWC«TSALT
CCMMON/L15/ TIT<30) .TC .OTOT. IT , IL.NT
COMMON/LIT/ XXX{30) ,C1 ( 30 ) .C 2( 30> ,C3<30 ) ,C4 (30) ,C5<30) ,C6( 30)
MM=10
NM1F=CCUUMN/CZ
IF(N-NMIF) 10.5.20
5 RETURN
10 IF(N.GT.580) RETURN
IFC ABS«THCN-20)-THKtN) .UT. 0.00 20) RETURN
NNNN=NI»lF-«-2
CALL MCISO(NP1 .NNNN)
DO 16 I-KF1.KNNN
OO 17 K = l.f>X
IFf HI I ).GT.KC«K+1) ) GO TO 18
17 CONTINUE
18 CAPO )=CAPC(K)
16 CONTINUE
20 N=NM1F
KM1=N-1
NM2=N-2
NP1=N+1
NP2=N*2
RETURN
END
94
-------
SUBROUTINE SEC*
COHMON/L1/ TH.CORGNC81«).CNC2(810),
*VP<810).DISFCCeill
COMWCN/L2/ AA«ei«), EE< 6 10 ) . CC< 6 1 * ) . R{ 61 O ) . x< 6 IP )
COMMON/L3X N.NK1.NP2.NP11 NP2
COMMCN/L4/ ALPHA,BETA.CT.DZ
COMMON/US/ FKO.KK1,RK2.RK3.RK4.RK5
COMMCN/L6/ SFLV.X.CSKH4 , CSNO3
COMMCN/C7/ BCU
COMMON/US/ DISPiTHMAX.THMIK
CCMMON/L9/T I I>E . TPR I NT . TMR ITE
COMMCN/L10/ H,CCK(81CI.CAP(810)
COMMONXL11/ THC(*0) .HCf «C ) ,CAPC («P> >
COMMCN/L12/ AC.BC.NX.NX1.CONST
CCMMON/L13X kFLUX(BlR)
COMMON/CIA/ VO.TMC.TSALT
IF(SFLCX.GT.C.CI GO TC 5
CONS=AC*EXP(BC*«TH{I)+TH(2))*0.5")
ADJ=OZ*<1.P-SFLUX/CCNS)
MCI>=H(2I-ACJ
IFIH< 1) ,LT.I-30r»50.1) Kl J
RETURN
CONTINUE
Hit >=H( 1)*1.40C
IFIH(l).GT.C.C) Hll)=«.0
RETURN
END
SUBRCUTIN= G4SCRG
COMMON/LI/ TH<81«) ,CKH4( 8 1 o ) .C NO3( 8 1 "» . CORGN{ 810 ) , CN02( 8 1 1 1 .
;<
COMMCN/L2/ AAI619).ea(eir).CC(61?).R(610),X(610)
COMMCN/L3/ N .Nfl ,M»2.NP1,NP2
COMMCN/L4/ ALPHA. BET*. CT.DZ
COMMON/LS/ PKO.RK1 . PK2 . RK3 . RK.4 . HK5
COMMCN/C6/ SFCUX.CSNH4.CSNO3
COMMON/L7/ POU
COMMCN/L8/ CISP.THMAX.THMIN
COMMON/I. 10/ H(eiC) ,CCNieiO)tCAP«81C)
CCMXCN/L13/ KiFLUXlal^)
COMMCN/L14/ VO.TfcC.TSALT
DO 5 1=1. NP1
ZK3 = ZZ 3 ( PK 3 . TH < I > , H < I ) , Z , T IME )
Z=COPGN«I1/CORGN(1 >
ZK5=ZZ5IRK5.TMI I ) , H( I ) . Z .T I ME )
CORGN1 I >=CCfiGMI )**RK2*CNO3< I »+TM( t »*RK4*CNH4< I 1-
*<»OU *ZK3*COBGNl I > >
CNO2(I )=C^C2CI )+*CNO3( I )
CONTINUE
RETURN
END
95
-------
SUBROUTINE GRAPH
COMMON/LI/ TH( 61 ?) ,CNH4< 81 0 ) ,C NO3 C 81 0 » ,CORGN< 810 > . CNO2 (8 1 0 ) t
*VP<810»,CISFC<810>
COMMCN/L3/ h .KM ,M»2,NF1 .NP2
COMMCN/L4/ /»LPf-A,BETA.DT,DZ
COMMCN/L16/IC. IWT
COMMON/1.18/ TGfiAPH<15) .NTGR.ITGR
IF{ ITGR.GT.hTGR) RETURN
CALL LINE*T
X1=X1*1.0
CONTINUE
CALL PLOT<0.0,YL.-3)
Xl = ->.0
OO 2" I-t>KKK.KK
YS=CNH4C D/20.0
CALL SYMBOL(XS.YS.£YMSZ.IC.O.O.-2>
20 CONTINUE
CALL PLOT«>L .-YLt-3)
xi = o.r>
OO 30 I=1.KKK.KK
YS=CORGM I )/!0.0
XS=X1/10.0
CALL SYMBOL
-------
SU3RCUT1NE *XISPL
COMMCN/L16/IC. I*T,
XL=14.0
XSt ZE = 1
YSt ZE1=6.01C •
YSIZE2=e.01C
CALL PLCTS^eO.r.-
CALL PLCTU.O.l.^,
CALL LINE»T(I»T)
CALL AXlS^J.O.O.O.
CALL AXIS(O.O ,c." .
CALL PLCT("»0»VLt-
CALL AX1S(C .r,C.",
CALL AXIS
« DEPTH tCM«
« NH4-K.MG1
3>
'CEPTHtCM*
CRG.NtMG'
3)
« CEPTH.CM*
'NC3-N.MG*
-3>
t-8 ,XS t ZE i 0. C ,0.0 , 10 .0 )
.3.YS!ZEi,9r< .0.0.0,0.10)
.-8,XSIZE,0.f>,«.0,10.r')
.8 . VSI ZE2 .9^
t-8 ,XS I ZE.O .0,0 .C . 10 .0 )
18 . VSI ZEl .90 .*> .« .0. 10. A )
.-a.xsize.o.o,i.i*,io.* )
.3 . YSI ZF2.9«.f> .0 .0,20.")
LEVEL 21
MAIN
DATE
77097
19/33/46
KG ISO ( I 1 . 12 )
TM(RIO) ,CNH4(B1« ) ,CNO3 ( 8 1 C > ,CORGN< 810 » . CNO2( * 10 ) .
SUBROUTINE
COMMCN/L1/
*VP( 810)
COMMON/L3/ fc.Kfl .N*2«NF1*MP2
CCMMCN/L4/ 4LPI-A.BETA.CT.DZ
COMMON /L1 1/ M813I ,CCN(810> ,CAP{810I
COMKCN/L17/ XXX(3">) ,C1 (30) ,C2( 30). C 3(3") ,C4( 3^) .C5 ( 30 ) .CC( SO
1=1
OQ 20 K=I1,I2
A=OZ* ) / ( XXX ( 1*1 ) -XXX( I ) ) )
CN03(K)=C4( I )+(A-XXX( I ) )*((C4( I+1)-C4( I ) )/(XXX( I+1)-XXX(I) ) )
CORGNIK )=C5(I )*(A-XXX(I))*((C5( 1*1 )-C5( I ))/(XXX( I+1)-XXX( I) ))
CORGN(K)=5C.CP/EXP(".0250*OZ*K)
CN02(K) = C6
-------
SUBROUTINE OUTPUT
COMMCN/L1/ imei*) .CNH4(81*>) ,CNO3( 81 0 I . CORGN (810 ) . CMC 2 (8 1 0 1 ,
*VO{810>.DISFC(8i:U
COMMCN/L2/ AM6IO),EE(CI0>,CC<610).R(610).X(6lf>)
CONMON/L3/ K.NM1,NM2.NP1.NP2
COMMCN/L4/ ALPHA.9eTA.CT.OZ
COMMON/IS'/ FKO.RK1 .FK2.PK3.RK4.ftK5
COMMON/L6X SFLLX.CSSH4.CSNO3
CONMGN/L7/ FCU
COMKCNXL8X CISF,THM*X.THMIN.HMIN.CCRGNI
COMMON/L9/TIKE.TPRIK T.TtaPITE
COMMON/L 10/ I- ( 810 ) . CCN (810). CAP( 81 ^ >
COMMONXL11/ THC«4'» ,HC(40>.CAPC(4C»
COMMON/LI 2X AC.BC.NX.NX1.CONST
CCMMON/L13/ tFLUXtai?!
COMMON/H4/ VO.tWO.TSALT
. COMMCN/L15/ TITO^I .TC.OTDT, IT, IL.NT
100 FQRMATCl' )
200 FORMAT(//X.SOX,«TTWF = •,E12.5X/.4X.•DEPTH.CM•,4X.•SUCTION.CM«,
-*4X.'THETA*,7X.«HYDR.CCKD.'.T56.'WATER FLUX*.
$T72.'NH4«,T6£.«NO3'.T?7.•CORGN'.5X.' NO2')
400 FORMAT(1"E12.4)
«IRITE(6.10'?I
TIME=TC
*RITE(6,2CO> TIME
DO 2« 1=1.NF1
ZZ=( 1-1 )*OZ
WRI TE(6.40C) ZZ.H{ I ),TH(I ) ,CDN( I ).WFLUX( I).CNt-4( I>,CNO3( I),
*CORGN(I).CNC2(I»
20 CONTINUE
' CALL TINT
IT=IT+1
IF( IT.GT.NT ) STOP
TC=TIT(IT)
OT=OTDT
ALPHA=OT/(2,C*CZ*CZ)
aETA=DTXDZ
25 CONTINUE
KK=2
TTT=CCKSTXCAPC(1)
TTT=TTT*ALPHA
IF(TTT.LE.2.00) GC TC 3T
RFTUPN
30 CONTINUE
DZVO=0.5«*D2/( VP(l<*)/Th< 1O) )
IF( (OT*KK1 .LT.CZV) OT=DT*KK
ALPHA=OTX(2.0*CZ*DZ)
8ETA=OTXDZ
RETURN
END
98
-------
APPENDIX D
KINETIC RATE COEFFICIENTS FOR THE NITROGEN TRANSFORMATIONS
A literature search was conducted to determine the magnitude
and differences in the first order transformation rate coefficients
observed by various research groups. Transformation rate co-
efficients are used in the simulation models presented in this
report (Sections 4 and 6) . The values, listed in Table 3, are
intended to serve as a guide in estimating the rate coefficients
for a given soil type. The reader is also referred to the re-
gression equations developed by Dutt et al.28 which relate
selected soil properties to the rate coefficients. The following
comments should be taken into account in utilizing Table 3.
(1) The rate coefficients given in Table 3 were, in most
cases, obtained from laboratory studies where "ideal" environ-
mental conditions for the transformation being investigated were
maintained (e.g., in the denitrification study of Cooper and
Smith98, the atmosphere in the incubation vessel was replaced
by 100% He and a supplementary carbon source was added to the
soil).
(2) In most experiments dealing with nitrogen transformations
in soils, only the resulting or net effects of several simultaneous
reactions can be measured. When two processes (such as minerali-
zation and immobilization) are working in opposite directions,
the difference between these reactions is measured by a net
increase (if mineralization prevails) or net decrease (if immo-
bilization prevails) in the NHn and N03 concentrations. It is
possible that although the opposing processes are both vigorous
and extensive, the net effects may be small. Thus, in a majority
of the laboratory studies, the net result of several simultaneous
reactions has been attributed to a single transformation process.
Isotope tracer studies105~1l° using 15N have been, however, help-
ful in overcoming these drawbacks.
(3) The mineralization-immobilization rate coefficients
listed in Table 3 were based on soil organic matter data. The
uniformity in the composition and degradation rate of this
innate material appears to be fairly well-established (e.g.,
data of Stanford and Smith16 and Stanford et al. ). Because of
the complexity of the composition of plant residues and animal
wastes, it may be necessary to simulate transformations of their
99
-------
individual components (e.g. Hagin and Amberger13, Beek and
Frissell11*, van Veen111, Browder and Volk11*). The values of
rate constants for mineralization of organic nitrogen to nitrate-
N as well as rates of NHa volatilization in manure treated soils
have been compiled by Reddy et al.113.
(4) Several investigators18'20 have reported that denitri-
fication follows zero-order kinetics. Bowman and Focht21 have
pointed out that many of these studies were conducted at high
nitrate concentrations, where zero-order kinetics may be expected
(as the substrate is non-limiting). Reddy et al.111* suggested
that results from many laboratory incubation experiments dealing
with denitrification follow psuedo-first-order kinetics when
in fact the reaction kinetics were zero-order. They attributed
this to a diffusion-controlled supply of NKn and/or NO3 to the
"active" denitrification zones in soils.
100
-------
TABLE 3. KINETIC TRANSFORMATION RATE COEFFICIENTS FOR VARIOUS NITROGEN SPECIES
IN SELECTED SOILS
PROCESS
SOIL TYPE
RATE COEFFICIENT EXPERIMENTAL
(day-1) CONDITIONS
REFERENCE
Mineralization;
OM -*• NKU
OM -»• NHi,
Chester silt loam 0.0073
Hagerstown silt loam 0.0078
Laboratory incubation at
20°C, carbon supplement
added.
101
OM •*• NH<,
OM
OM -*-
Salinas clay
0.001
29 soils with a wide 0.0077
range in properties
11 soils with a wide 0.001 -
range in properties 0.0078
Laboratory incubation at
24°C, 100% relative 12
humidity. Data of Broad-
bent et al.9 7 .
Laboratory incubation 16
at 35°C.
Laboratory incubation at
temperatures ranging from 17
5° - 35°C.
Immobilization;
-* OM
NO 3 + OM
Ontario loam
Ontario loam
0.15
0.15
Laboratory incubation at
30°C. Carbon supplement,
data of Stojanovic and
Broadbent10°.
12
Nitrification:
NH.T •* NO2
Salinas clay
0.22
Laboratory incubation at
24°C and 100% relative
-------
TABLE 3. Continued
PROCESS
SOIL TYPE
RATE COEFFICIENT EXPERIMENTAL
(day-1)
CONDITIONS
REFERENCE
N02
H
O
N02
-»• NO 3
-»• N02
* N03
* NO 3
-»• NO 3
NHi, -»• NO 3
NH^ ->• NO3
Denitrification:
NO3 ->• N02
Salinas clay
Milville loam
Milville loam
Tippera clay loam
Columbia silt loam
Columbia silt loam
9.0
0.143
9.0
0.0033
0.0543
0.24 -
0.72
Hanford sandy loam 0.76 -
1.11
Columbia silt loam 0.24 -
0.62
N03 ->• (N2 + N20) Yolo loam
0.024
1.08
0.004
0.032
humidity. Data of Broad- 12
bent et al.97.
Laboratory incubation at
22°C, 1/3-bar and 1-bar 12
water contents. Data of
Justice and Smith9 9.
Laboratory incubation at
temperatures ranging from 26
20-60°C.
Steady-state flow through
soil column maintained at 15
-85 cm suction.
Steady-state flow through 103
soil column, used 15N.
Steady-state and transient
concentration profiles in 102
soil column, used 15N.
Steady-state flow through
soil columns. O2 level 15
ranged from 0 to 25%.
Laboratory soil columns, 104
used 15N.
-------
TABLE 3. Continued
RATE COEFFICIENT EXPERIMENTAL
PROCESS SOIL TYPE (day-1) CONDITIONS REFERENCE
NO 3 -*• N02 Hanford sandy loam 0.04 -
0.075
k
NOs •»• (Na + N20) Columbia silt loam 0.048 -
0.192
Steady-state flow through , ~.^
soil columns, ised N.
Transient and steady-state
concentration profiles in 102
soil columns.
o
U)
-------
APPENDIX E
LIST OF PUBLICATIONS RESULTING FROM THIS PROJECT
1. Rao, P. S. C., H. M. Selim, J. M. Davidson, and D. A. Graetz.
1976. Simulation of transformations, ion-exchange, and
transport of selected nitrogen species in soils. Soil Crop
Sci. Soc. Florida Proc. 35:161-164.
2. Rao, P.S.C., J. M. Davidson, and L. C. Hammond. 1976.
Estimation of nonreactive and reactive solute front loca-
tions in soils. in Residual Management by Land Disposal.
Proc. of Hazardous Waste Res. Symp. Tucson, Arizona. EPA-
600/9-76-015, p. 235-242.
3. Selim, H. M., J. M. Davidson, and P. S. C. Rao. 1977.
Transport of reactive solutes in multilayered soils. Soil
Sci. Soc. Amer. J. 41:3-10.
4. Selim, H. M., J. M. Davidson, P. S. C. Rao, and D. A. Graetz,
1977. Nitrogen transformations and transport during trans-
sient unsaturated flow in soils. (submitted to Water Resour,
Res.) Presented at the 68th annual meetings of Ann. Soc.
Agron., Houston, TX.
5. Selim, H. M. and J. M. Davidson. 1977. Numerical solution
of nitrogen transformations and transport equations during
transient unsaturated flow in soils. SHARE Program Library.
6. Davidson, J. M., P. S. C. Rao, and R. E. Jessup. 1977. A
critique of the paper "computer simulation modeling for
nitrogen in irrigated cropland" by K. K. Tanji and S. K.
Gupta. in. Nitrogen and Soil Environment. D. R. Nielsen
and Judy McDonald, eds. Academic Press, N.Y. (in press)
7. Davidson, J. M., P. S. C. Rao, and H. M. Selim. 1977.
Simulation of nitrogen movement, transformations and plant
uptake in the root zone. Proc. of National Conf. on Irri-
gation Return Flow Quality Management. Fort Collins, Colo.
p. 9-18.
8. Rao, P. S. C., R. E. Jessup, and J. M. Davidson. 1977. A
simple model for description of the fate of nitrogen in the
crop root zone. Submitted to Agron. J.
104
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9. Rao, P. S. C., P. V. Rao, and J. M. Davidson. 1977. Estima-
tion of the spatial variability of the soil-water flux. Soil
Sci. Soc. Amer. Jour. Vol. 41 (in press).
105
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing}
1. REPORT NO.
EPA-600/3-78-029
2.
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
Simulation of Nitrogen Movement, Transforma-
tion, and Uptake in Plant Root Zone
5. REPORT DATE
March 1978 issuing date
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
James M. Davidson, Donald A. Graetz, P. Suresh
C. Rao, and H. Magdi Selim
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
University of Florida
Gainesville, FL 32611
10. PROGRAM ELEMENT NO.
1BB770
11. CONTRACT/GRANT NO.
R803607
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Research Laboratory—Athens, GA
Office of Research and Development
U.S. Environmental Protection Agency
Athens, GA 30605
13. TYPE OF REPORT AND PERIOD COVERED
Final. 3/10/75-3/9/77
14. SPONSORING AGENCY CODE
EPA/600/01
15. SUPPLEMENTARY NOTES
16. ABSTRACT
A detailed research model and a conceptual management model were
developed to describe the fate of nitrogen in the plant root zone. Pro-
cesses considered in both models were one-dimensional transport of water
and water-soluble N-species as a result of irrigation/rainfall events,
equilibrium absorption-desorption, microbiological N-transformations, an<
uptake of water and nitrogen species by a growing crop.
The research model was based on finite-difference approximations
(explicit-implicit) of the partial differential equations describing one'
dimensional water flow and convective-dispersive NH. and NO- transport
along with simultaneous plant uptake and microbiological N-transforma-
tions. Ion-exchange (absorption-desorption) of NH. was also considered.
The micro-biological transformations incorporated into the model describ*
nitrification, denitrification, mineralization and immobilization. All
transformations were assumed to be first-order kinetic processes.
The management model consists of several simplifying assumptions
requiring minimal input data. The model provides an integrated descrip-
tion of the behavior of various nitrogen species in the plant root zone.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
COSATI Field/Group
Simulation
Fertilizers
Nitrogen
Mathematical models
Plant nutrition
Agricultural
chemicals
Modeling
Nitrogen compounds
68D
72E
98A
8, DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (ThisReport)'
UNCLASSIFIED
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
!1. NO. OF PAGES
116
22. PRICE
EPA Form 2220-1 (9-73)
106
4U.S. SWBIMIBITIWmKOfflCfc 197J- 260-880 A6
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